UTA-HEP/LC-0001

SIMULATION STUDIES OF A NEW DIGITAL HADRONIC CALORIMETER,

USING GAS ELECTRON MULTIPLIER (GEM) DETECTOR

The members of the Committee approve the master’s thesis of Shahnoor Habib

Jaehoon Yu Supervising Professor __________________________________

Andrew White __________________________________

Andrew G. Brandt __________________________________

UTA-HEP/LC-0001

SIMULATION STUDIES OF A NEW DIGITAL HADRONIC CALORIMETER,

USING GAS ELECTRON MULTIPLIER (GEM) DETECTOR

by

SHAHNOOR HABIB

Presented to the Faculty of the Graduate School of

The University of Texas at Arlington in Partial Fulfillment

Of the Requirements

For the Degree of

MASTER OF SCIENCE IN PHYSICS

THE UNIVERSITY OF TEXAS AT ARLINGTON

August 2003

UTA-HEP/LC-0001

iii

ACKNOWLEDGMENTS

I would like to thank my graduate committee – Dr. Andrew Brandt and

Dr. Andy White for suggesting new ideas for the research.

I would take this opportunity to thank Dr. Mark Sossebee for being there

whenever I needed help regarding problems on my computer, or bugs in my

code, or going over work I had already done. I enjoy discussing the issues

arising in research with him and getting his feedback.

Many thanks to Venkat Kaushik for installing the tools that I used for

analysis and getting me over some tough PowerPoint problems. Last but not

least, I would like to thank Barry Spurlock and Pervaz Allaudin for reading my

thesis and making comments on it. Though Dr. Kaushik De and Dr. Asok Ray

were not on my committee, they were very helpful, Dr. De for his sound advice

that kept my sanity in check and Dr. Ray for encouraging me to enroll in UTA

and being my advisor whenever I needed him.

Last but least I thank Dr. Yu, who supervised my work, for having such

confidence in my abilities and also in getting me the research assistantship for

the summer semester so that I can concentrate on my thesis.

August 31, 2003

UTA-HEP/LC-0001

iv

ABSTRACT

SIMULATION STUDIES OF A NEW DIGITAL HADRONIC CALORIMETER,

USING GAS ELECTRON MULTIPLIER (GEM) DETECTOR

Publication No. ______

Shahnoor Habib, M.S

The University of Texas at Arlington, 2003

Supervising Professor: J. Yu

A central feature of the Standard Model of elementary particle physics is

the “Higgs mechanism.” The particle responsible for mediating this interaction is

called the Higgs boson. Among the possible decay channels of the Higgs are

multi-jet final states, for example, via the reaction bbjjhZee →→−+0 . Thus

Higgs searches require calorimetry with excellent energy and position

resolution. One technique used to improve jet energy resolution, the “energy

flow” algorithm, will dramatically increase the cost of detector readout

electronics unless a digital rather than analog readout technique can be

implemented. The advent of high luminosity accelerators colliding particle

beams at the TeV energy scale demands fast, high performance position-

UTA-HEP/LC-0001

v

sensitive detectors. The Gas Electron Multiplier (GEM) concept, developed by

Sauli et al in the 1990’s, can satisfy all of these requirements.

This thesis presents simulation studies of a GEM-based calorimeter for a

−+

ee linear collider. Output from the simulations was analyzed in the ROOT/C++

framework. Various studies were undertaken to gauge the feasibility of using

GEM as the sensitive gap of a sampling calorimeter. This thesis also measures

its energy response and resolution to incident pion beams in analog and digital

readout modes.

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vi

TABLE OF CONTENTS ACKNOWLEDGMENTS................................................................................ iii ABSTRACT.................................................................................................... iv LIST OF ILLUSTRATIONS ............................................................................ vii LIST OF TABLES ......................................................................................... xi LIST OF ABBREVIATIONS ........................................................................... xiii Chapter 1. INTRODUCTION............................................................................... 1 1.1 Introduction to Standard Model.......................................... 1 1.2 Tools in High Energy Physics Experiments....................... 2 1.3 Challenges of High-Energy Physics................................... 3 1.4 Thesis Organization........................................................... 6 2. CALORIMETRY................................................................................. 7 2.1 Introduction......................................................................... 7 2.2 Features of Calorimetry ..................................................... 8 2.3 Types of Calorimeters........................................................ 9 2.4 Energy Response of a Calorimeter.................................... 10 2.5 Energy Resolution of a Calorimeter................................... 12 2.5.1 Fluctuations in Electromagnetic Showers.............. 13 2.5.2 Fluctuations in Hadronic Showers.......................... 14 2.5.3 Determination of Resolution................................... 14 2.6 Readout in Calorimetry...................................................... 15

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2.6.1 Readout in Electromagnetic Calorimeters.............. 15 2.6.2 Readout in Hadronic Calorimeters......................... 15 2.7 Techniques to Improve Jet Energy Resolution.................. 16 3. GAS ELECTRON MULTIPLIER (GEM) AS A DRIFT CHAMBER...... 19 3.1 Introduction......................................................................... 19 3.2 GEM Detector and its Role ................................................ 20 3.3 Basic Structure................................................................... 21 3.4 Formation of Avalanche in GEM........................................ 22 3.5 Discharge and Breakdowns in GEM.................................. 24 3.6 GEM in Various Combinations........................................... 25 3.6.1 Single GEM operation ............................................ 25 3.6.2 GEM+MSGC........................................................... 26 3.6.3 Double GEM Detector ............................................ 26 3.6.4 Triple GEM Detector............................................... 27 3.7Advantages of GEM............................................................ 28 4 MONTE CARLO TOOLS.................................................................... 29 4.1 Introduction......................................................................... 29

4.1.1 Conclusions Based on the Results of Simulation........... 30 4.2 GEANT4 – Detector Simulation Program .......................... 31 4.3 Mokka – Detector Simulation Program .............................. 32 4.3.1 Description of Mokka TDR Model........................... 32 4.3.2 Electromagnetic Calorimeter.................................. 34

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4.3.3 Hadronic Calorimeter.............................................. 35 4.3.4 Generation of Primary Events ................................ 35 4.4 Mokka GEM........................................................................ 35 4.5 ROOT for Analysis ............................................................. 38 5. STUDY OF SINGLE PIONS................................................................ 39 5.1 Analog Studies Using Mokka TDR..................................... 39 5.1.1 Systematic Error and Their Effects on the Fit ........ 44 5.2 Analog Studies Using Mokka GEM.................................... 46 5.3 Mokka GEM Digital Analysis.............................................. 56 5.3.1 Feasibility of Digital Use of GEM............................ 56 5.3.1.1 Plateau effect and Cell Occupancy..................... 58 5.4 Muon Study ........................................................................ 64

5.5 Effect of Threshold Cut on the Response and Resolution of the Digital Calorimeter.............................................................. 67 5.6 Leakage and its Effect on the Response and Resolution of the Digital Calorimeter.............................................................. 69 5.7 Energy and Number of Cells Hits Distribution.................... 72

6. CONCLUSIONS.…………………………………………………………. 77

Appendix

A. MOKKA............................................................................................. 77

B. PROGRAMS USED IN THE ANALYSIS............................................ 82

C. GEM MANUFACTURING TECHNOLOGY........................................ 109

D. REMAINING PLOTS........................................................................... 111

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ix

E. FITS USED IN THE ANALYSIS ...................................................... 118

F. TESLA ................................................................................................. 120

G. TABLES............................................................................................... 122

REFERENCES ............................................................................................ 129

BIOGRAPHICAL INFORMATION ............................................................... 131

x

LIST OF ILLUSTRATIONS

Figure Page 1.1 Fundamental particles in Standard Model .................................................2

2.1 A typical modern detector..........................................................................9

2.2 The interaction of various particles with the different components of a detector ............................................................................................................10 3.1 GEM with XY readout ................................................................................ 21

3.2 Schematic view of a GEM detector. The drift space is 3 mm and the induction gap is 1 mm thick.............................................................................. 22 3.3 The electric field in a GEM microhole........................................................ 23

3.4 Single GEM................................................................................................ 25

3.5 Single GEM with MSGC............................................................................. 26

3.6 Double GEM detector ................................................................................ 27

3.7 Triple GEM detector................................................................................... 27

4.1 Primary detector dimensions. Green shows ECAL, yellow is HCAL and blue is structure containing the magnetic coils........................................................ 34 4.2 The ECAL has eight staves and each stave contains five modules..........34

4.3 Mokka TDR – Sensitive layers in hadron calorimeter................................36

4.4 Simple GEM and detailed GEM. Courtesy of Venkat................................ 36

4.5 Energy distribution for 75 GeV pions using detailed geometry (blue) and simple geometry (magenta)............................................................................. 37 4.6 Gain at 420=∆V Volts for a Double GEM................................................. 37

xi

5.1 Total live energy distribution for 50 GeV pions in the Mokka TDR with the result of a gaussian fit to the data.................................................................... 42 5.2 Mokka TDR response curve fitted with a linear function........................... 43

5.3 Converted energy distribution for 50 GeV Pions in the Mokka TDR......... 43

5.4 Resolution curve for single pion detection of Mokka TDR with systematic errors…............................................................................................................ 44 5.5 Resolution curve for single pions using the Mokka TDR with systematic errors multiplied by two.................................................................................... 45 5.6 Plot A) is the ECAL signal, B) is the HCAL signal. Plot C) shows the energy distribution for events that did not fall into either the ECAL or HCAL plot. Plot D) shows the total signal for 10 GeV pions .......................................................... 48 5.7 Energy distribution in the ECAL and HCAL for 50 GeV pions...................49

5.8 Signal distribution for showers induced by 50 and 75 GeV pions in the ECAL, respectively. Fit on the data is gaussian.............................................. 51 5.9 Calculation of the weighting factor. Top plot shows the response of ECAL and the bottom is the response curve for HCAL.............................................. 52 5.10 Total live energy distributions for 50 GeV pions after taking into account the difference in HCAL and ECAL responses with two different ranges for a gaussian fit....................................................................................................... 53 5.11 Response curve for Mokka GEM............................................................. 54

5.12 Total converted energy distributions for 50 GeV Pions. Two different ranges for a gaussian fit are shown................................................................. 55 5.13 Resolution curve for Mokka GEM [Table G-5b] ....................................... 56

5.14 Mean numbers of cells hit vs. incident pion energy................................. 57

5.15 Number of cells hit vs. energy deposited in Hcal Only............................58

xii

5.16 Cell occupancy for 3 GeV pions in Mokka GEM...................................... 59

5.17 Cell occupancy for 100 GeV pions in Mokka GEM.................................. 60

5.18 Relationship between energy deposited per event E vs. numbers of cells per event N. The top is the profile histogram of the bottom 2-d histogram ..... 61 5.19 Weighting factor – digital study for Mokka GEM. The top shows the response curve for ECAL, while the bottom plot shows the response curve for HCAL…............................................................................................................ 62 5.20 Response curve for digital study – Mokka GEM...................................... 63

5.21 Resolution curve – digital study for Mokka GEM..................................... 64

5.22 Determination of threshold from the cell energy distribution of muons in HCAL of Mokka GEM....................................................................................... 65 5.23 Correlation between efficiency and threshold for 100 GeV muons in HCAL of Mokka GEM....................................................................................... 66 5.24 Calculation of dE/dN ................................................................................ 67

5.25 Weighting factor for Mokka GEM with threshold 0.23 MeV.....................68

5.26 Response curve for Mokka GEM with threshold applied......................... 68

5.27 Resolution in Mokka GEM with threshold applied ................................... 69

5.28 Fractional energy distribution in layer 40 in HCAL of Mokka GEM......... 70 5.29 Distribution of energy deposited in 40 layers of HCAL ............................ 71

5.30 Energy distribution (MeV) in layer number 40 in HCAL of Mokka GEM.. 71

5.31 Energy distributions in 40 layers in HCAL of Mokka GEM......................72

5.32 Distribution of number of cells hit in 40 layers in HCAL of Mokka GEM.. 73

D.1 Weighting factor for Mokka TDR, HCALECAL EEW /= ...................................111

xiii

D.2 Response curve for Mokka GEM with threshold applied. The black curve in the top shows a cubic fit while in the bottom plot a quartet fit is shown in black. Blue line shows a linear fit in both plots...........................................................112 D.3 Weighting factor for Mokka GEM with threshold applied..........................113

D.4 Energy distribution of 50 GeV pions using range (0,Xmax) where Xmax is the maximum datum in the data set.......................................................................113 D.5 Energy distribution of 50 GeV pions using range for the best dof/2χ fit .114 D.6 Response curve of Mokka GEM - digital study with threshold applied. A nonlinear approach..........................................................................................114 D.7 Distribution of converted energy for 50 GeV pions – the top plot employs (0,Xmax) range and the bottom plot employs the best dof/2χ range..............115 D.8 Resolution of Mokka GEM – digital study with threshold applied. A nonlinear approach..........................................................................................116

xiv

LIST OF TABLES Table Page 5.1 Example of Mokka script file……………………………………………….39 5.2 Strategy for selecting events for ECAL and HCAL………………………47 6.1 Compilation of fit parameters for response and energy resolution for TESLA TDR and GEM……………………………………………………………..75 A.1 Sample of ECAL hits file……………………………………………………78 A.2 Sample of HCAL hits file……………………………………………………78 G.1 Mokka TDR - Response Data...............................................................122

G.2a Mokka TDR - Resolution Data............................................................122

G.2b Mokka TDR - Resolution Data............................................................122

G.3 Mokka GEM - Weighting Factor............................................................122 G.4 Mokka GEM - Response Data..............................................................123

G.5a Mokka GEM - Resolution Data ...........................................................123

G.5b Mokka GEM - Resolution Data ...........................................................123

G.6 Mokka GEM - Feasibility of Digital Study..............................................123 G.7 Mokka GEM - Weighting Factor – Digital Study....................................124 G.8 Mokka GEM - Response Data – Digital Study......................................124

G.9a Mokka TDR - Resolution Data – Digital Study....................................124

G.9b Mokka TDR - Resolution Data – Digital Study....................................125

G.10 Mokka GEM – Data for the Calculation of Weighting Factor - Digital Study With Threshold.......................................................................................125

xv

G.11 Mokka GEM - Response Data - Digital With Threshold....……………125

G.12a Mokka GEM – Resolution Data - Digital With Threshold.…..……….126

G.12b Mokka GEM – Resolution Data - Digital With Threshold…..………..126

G.13 Mokka GEM - Response Data - Digital With Threshold – Nonlinear approach..........................................................................................................126 G.14a Mokka GEM – Resolution Data - Digital With Threshold – Nonlinear approach..........................................................................................................127 G.14b Mokka GEM – Resolution Data - Digital With Threshold –Nonlinear approach..........................................................................................................127 G.15 Mokka GEM - Leakage Data - Without Threshold……….…………….127

xvi

LIST OF ABBREVIATIONS

TESLA Tera Electron volts Energy Super conducting Linear Accelerator

SIT SILICUM INTERMEDIATE TRACKER

FTD THE FORWARD TRACKING DISKS

VXD THE VERTEX DETECTOR

ECAL ELECTROMAGETIC CALORIMETER

HCAL HADRONIC CALORIMETER

GEM GAS ELECTRON MULTIPLIER

LHC LARGE HADRON COLLIDER

NLC NEXT GENERATION LINEAR CALORIMETER

MSGC MICRO-STRIP GAS CHAMBER

MPD MICRO-PATTERN DETECTOR

TPC TIME PROJECTION CHAMBER

EM ELECTROMAGNETIC

GEANT GEometry ANd Tracking

1

CHAPTER I

INTRODUCTION

1.1 Introduction to Standard Model Experimental High-Energy Physics is the study of the fundamental

constituents of matter and their interactions. The mission is to understand the

nature of matter at its most fundamental level and to explore the evolution of the

universe through these fundamental interactions of matter. In a typical

experiment, particles like protons or electrons are accelerated to very high

energies and brought into head-on collisions, creating a variety of other

particles, which do not normally exist in nature. Detailed studies of this ‘particle

zoo’ have revealed an inner order which is amazing in its simplicity: matter in all

its forms, from stars to living organisms in the universe, is made up of six

quarks and six leptons interacting among themselves by exchanging gluons,

photons, or W and Z particles, following strict rules coded into the current

theoretical framework, the Standard Model [1,2,3,4,5]. Figure 1.1 lists the

fundamental particles in Standard Model.

2

Figure 1.1: Fundamental particles [6] in Standard Model

1.2 Tools in High-Energy Physics Experiments

The basis of physics is experimentation. Without it, physics would be

reduced to mere philosophic speculation. Experiments have made substantial

contributions that helped establish the Standard Model as the premier theory of

elementary particle physics. High-energy physicists rely on four essential

scientific tools [7]:

• Powerful accelerators to create high-energy particle collisions.

• Super conducting magnets constructed from advanced materials to

guide particle beams.

3

• Sophisticated particle detectors with extremely fast signal readout

technology to observe and record particle collisions.

• Innovative computing solutions to store, access and analyze large

quantities of data.

The chief instruments for performing modern particle physics are

accelerators and detectors. Accelerators accelerate beams of subatomic

particles or nuclei to adequate high energies to investigate fundamental

interactions. These accelerators come in two basic forms, circular and linear.

Without such appropriate instruments, however, it is not possible to do high-

energy physics experiments. This is the reason physicists have been

collaborating with each other since the 1980’s, designing and perfecting the

major parts of Large Hadron Collider (LHC) and Next Linear Collider (NLC).

Substantial resources have been invested on building prototype accelerators,

components and systems to test the state-of-the-art technologies required. The

GEM (Gas Electron Multiplier) detector is one of the components tested for its

possible use in the LHC experiments.

Detectors [8]

When colliding high-energy particles it is possible to create the

conditions necessary to explore the interior of matter and to create new types of

matter. To observe and identify the well-known particles and also the possible

new states of matter, very sophisticated detectors are needed.

4

Modern detectors consist of many different components. The aim of the

complex system of detectors surrounding the collision point is to:

• Identify the particles.

• Measure their energy and momentum.

• Determine their trajectories.

The type of particles produced, their energies and directions reveal the

underlying physics of interactions and the constituents of matter. The

components of the detectors are oriented so that the produced particles will go

through the different layers of the detector [see Figs. 2.1 and 2.2].

An experiment consists of a large number of detectors, each of them

having a well-defined task. Combining the information from all of them will

produce a detailed picture of what happened in the particle collision. There are

three main types of particle detectors:

• Tracking detectors to determine the trajectory of charged particles.

• Calorimeters to determine the energy of both charged and neutral

particles.

• Muon detectors to detect and identify muons.

Since my research involves Calorimetry, I have devoted a separate

chapter to describe calorimeters and their use in High Energy Physics

experiments.

5

1.3 Challenges of High-Energy Physics

Although the Standard Model is one of the most successful and thoroughly

tested theories in physics, it may not be the final answer. Many unsolved

mysteries suggest the need for ideas and mechanisms that go beyond our

present knowledge. The discoveries of the 21st century will require powerful

accelerators, world-class experiments and groundbreaking ideas to unravel the

secrets of matter, space and time. For example, experimentation at the LHC

presents unprecedented challenges. The intense proton beams intersect at 25

nanosecond intervals, with multiple collisions per crossings. As a consequence

of high particle fluxes, radiation damage to detectors and electronics could lead

to degradation of performance. The luminosity of the machine is extremely high

so that very rare interactions can be observed, but production of background

events will dominate by many orders of magnitude any possible signals of new

physics. Typical experimental scenarios are the production of fewer than 100

Higgs events per year relative to a raw background of 1015 events due to

“known physics processes.” [9]

As particle accelerators around the world continue to achieve higher

energies and instantaneous luminosities, detectors that are needed for the

study of the outcome of the collisions must be improved to disentangle and

decipher complex signatures that are densely packed in both space and time. In

measuring energies and directions of various particles emanating from the

6

interaction vertex, calorimeters play a key role in determining the success of

high-energy physics experiments.

1.4 Thesis Organization

Chapter two describes Calorimetry, the various types of calorimeters and

characteristic features of selected calorimeters around which my research

revolves. Chapter three introduces GEM detectors, their basic features,

principles of operation and their application in various forms. Chapter four

covers Monte Carlo tools. In chapter five, the simulation data analysis is

discussed. Chapter six concludes the work done and the direction in which the

work will progress. Finally the appendices contain various supplementary

materials, for example, additional plots, tables containing data that was used for

plotting response and resonance curves, program codes, etc.

7

CHAPTER 2

Calorimetry

2.1 Introduction In nuclear and particle physics, Calorimetry refers to the measurement of

the energies of particles, through total absorption in a block of matter, called a

calorimeter. In the absorption process, almost all the particle’s energy is

eventually converted into heat, hence the term calorimetry. The most energetic

particles in modern accelerator experiments are measured in units of TeV

(1000GeV), whereas 1 calorie is equivalent to about 107 TeV. The rise in

temperature of the block that absorbs the particle is thus, for all practical

purposes, negligible.

Particles have electromagnetic or nuclear interactions in the matter they

pass through. The interaction usually creates an analog signal, which is

measured or converted into standardized pulses using fast electronics. For

example, in a scintillation detector, when electrons or photons are absorbed in

8

the medium, their entire kinetic energy is used to excite the atoms or molecules

of which this medium is composed. The excited atoms or molecules emit this

excitation energy in the form of visible light when returning to the ground state

and this scintillation light forms the basis of the calorimeter signals.

There are two types of calorimeters – total absorption and sampling

calorimeters. In a total absorption calorimeter, the entire detection volume is

sensitive to the shower particles and contributes to the signals it generates. In a

sampling calorimeter, different materials, called the passive and active medium,

respectively, exercise the functions of particle absorption and signal generation.

The passive medium is usually a high-density material, such as iron, copper,

lead or uranium. The active medium generates the light or charge that forms the

basis for signals from such a calorimeter [10]. Materials used for active medium

include silicon, polystyrene scintillator, liquid argon, etc.

2.2 Features of Calorimetry v Neutral and charged particles when incident on a block of material

deposit energy through creation and absorption processes.

v Energy loss mechanisms: pair production, ionization, bremsstrahlung,

the photoelectric effect and the Compton effect.

v Relative energy resolution improves with increasing energy, as σ/E is

directly proportional to n/1 and E/1 , where n is the number of

secondary shower particles and is proportional to the incident energy E.

9

v Longitudinal depth sufficient to contain the shower cascade increases

logarithmically with energy.

v Longitudinal and lateral development of showers is different for

electrons, photons, hadrons and muons.

v If the calorimeter has fine lateral and longitudinal segmentation then

efficient triggering on e/γ, jets and missing ET is possible.

2.3 Types of Calorimeters

The components of a calorimeter are arranged outside the beam pipe, in

a layered structure, rather like the layers of an onion. List of different layers are

shown in Fig 2.2.

Figure 2.1: A typical modern detector

10

Figure 2.2: The interaction of various particles with the different components of

a detector [12]

Among the different layers of detector, the calorimeter layers are as follows

[11]:

Electromagnetic Calorimeter: Measures the energy of electrons, positrons and

photons as they interact with the electrically charged particles inside matter,

and helps to discriminate between electrons, photons and hadrons.

Hadronic Calorimeter: Showers initiated by high-energy hadrons are measured

with a hadronic calorimeter, which is optimized for incident hadrons. A hadronic

calorimeter is normally placed behind the electromagnetic calorimeter, which

fully contains the electromagnetic showers. 2.4 Energy Response of a Calorimeter

Calorimeters not only detect the presence of radiation, but also are

capable of providing information about the energy of the radiation. This is

11

possible because the amount of ionization in a detector is proportional to the

energy a particle loses in the sensitive volume. If the detector is sufficiently

large such that the radiation is completely absorbed, then this ionization gives a

measure of the shower energy [13].

The response function of the detector is a function of the particle type

being detected. The spectrum of pulse heights (response) observed from the

detector when a monoenergetic beam of the given radiation bombards it is

shown in Fig. 5.1. Ideally, one would like to see a sharp delta-function peak for

a mono-energetic beam. Consider, for example, mono-energetic electrons,

incident on a detector thick enough to stop them. Assuming all the particles lose

their energy, the distribution of energy deposited is generally a gaussian peak.

In reality, however, some of the particles will scatter out of the detector before

fully depositing their energy. This introduces a low energy tail. Similarly some

electrons will emit bremsstrahlung photons that may escape from the detector,

corresponding to events at lower energy than the peak. If the tail is small,

however, this can still be a reasonable approximation to the ideal Gaussian fit

depending on the precision desired.

Since the entire kinetic energy of the showering electron or photon is

used to generate the secondary photons and electrons that constitute the

calorimeter signals, the calorimeter should be intrinsically linear for the

electromagnetic shower detection: a 20 GeV electron generates, on the

average, twice as many shower particles as a 10 GeV electron. Hence, if we

12

take the mean of the gaussian distributions and plot it against the incident

energy of the particles then, if the detector is linear, the mean corresponds

directly to the energy of the incident radiation [see Figs. 5.2, 5.11, 5.20, D.2 and

D.6].

2.5 Energy Resolution of a Calorimeter

Energy resolution is an important factor for detectors that are designed to

measure the energy of the incident radiation, since it determines the precision

with which the energy is measured. In particle physics experiments, a given

calorimeter signal is used to determine the energy of the particle that produced

it. In order to determine the energy of a detected particle, one needs to know:

v The relationship between the measured signals and incident energy (the

detector calibration or response of the detector).

v The energy resolution of the calorimeter.

The energy resolution determines the precision with which the unknown

energy of a given particle can be measured. Resolution is experimentally

determined from the precision with which the energy of particles with known

energy is reproduced in the calorimetric measurements.

In particle physics experiments, the energy resolution of the calorimeter

may be the factor that limits the precision with which the mass of new particles

can be determined. It may limit the separation between particles with similar

13

masses, for example, in the jet-jet decay of the intermediate vector bosons W’s

and Z’s.

The resolution is a function of the energy deposited in the detector.

Resolution improves with increasing energy. This is due to the poisson

statistical behavior of ionization and excitation. It is found that the average

energy required to produce an ion pair is a fixed number, called critical energy,

b, which depends only on the material. For energy E, on average, bEJ /= is

the number of ion-pairs produced in the detector. Thus as energy increases, the

number of ionization events also increases, resulting in smaller relative

fluctuations.

When high-energy particles are absorbed in a calorimeter, their energy is

degraded to the level of atomic ionizations or excitations that may be detected.

The precision with which the energy of the showering particles can be

measured is limited by:

1) Fluctuations in the processes through which the energy is degraded.

2) The technique chosen to measure the final products of the shower

cascade processes.

2.5.1 Fluctuations in Electromagnetic Showers:

In electromagnetic showers, fluctuations in the shower development

determine the ultimate limit on the achievable energy resolution. It also depends

on the technique used to measure the energy.

14

2.5.2 Fluctuations in Hadronic Showers:

Intrinsic fluctuations in hadronic showers lead to event-by-event

variations in the fraction of “visible energy,” that is, energy used to ionize or

excite the calorimeter’s atoms and/or molecules in the sensitive gap. The

intrinsic fluctuations dominate in a hadronic calorimeter to such an extent that

the chosen measurement techniques often have little or no effect on the

hadronic energy resolution. By a clever design of the readout, the effect of

these intrinsic fluctuations can be partially eliminated, for example, by using the

GEM detector. The decoupling of signal generation and readout in GEM makes

it possible to optimize the readout for the specific detector [see Figs. 3.4-3.7].

2.5.3 Determination of Resolution

Assume that a particle with energy E creates a signal S that, on average,

consists of n signal quanta (examples are scintillation or Cerenkov photons,

electron-ion or electron-hole pairs, etc.) [10]. Event-by-event fluctuations in the

detection of such particles correspond to poissonian (or gaussian, for n>5)

fluctuations in the number n. The relative width of the signal distribution,

σS/<S>, that is, the relative precision in the measurement of energy, σE/<E>, is

then equal to nnn /1/ = . If the calorimeter is linear, it will produce a signal

that consists, on average, of 4n quanta when it absorbs a particle with energy

4E. The relative precision, in the energy measurement energy of these

particles, amounts to nnn /5.04/4 = , which is a factor 2 better than that for

particles with energy E.

15

For a linear calorimeter, its resolution is described as EaEE // =σ ,

where the value of a represents sampling fluctuations. It is customary to

express calorimetric energy resolutions in terms of the value of a, with energy E

given in units of GeV. The relationship expresses the fact that the energy

resolution improves with increasing energy [see Figs. 5.4, 5.5, 5.13, 5.21 and

D.8].

2.6 Readout in Calorimetry Most modern calorimeters are sampling calorimeters, which measure a

fraction of the incident energy deposition with layers of high-density absorber

and active medium. The active layers are instrumented with readout and

therefore take a “sample” of the energy from shower particles.

Conventional calorimeters require readout of a wide dynamic range to

accurately measure energy deposited within the active medium. The necessity

of precision readout drives the cost of conventional analog calorimeter signal

readout.

2.6.1 Readout in Electromagnetic Calorimeters Showers initiated by electrons and photons proceed through

electromagnetic interactions that are well contained both longitudinally and

transversely, and thus have relatively small fluctuations in shower development.

16

For purely electromagnetic showers it is consequently possible to achieve good

resolution through the use of a sampling calorimeter with small readout cells.

2.6.2 Readout in Hadronic Calorimeters For hadronic showers or “jets,” energy and position resolution are limited

by several phenomena. First, the energy is spread over a much greater depth

and width. Second, larger statistical fluctuations in the development of the

shower introduce a large inherent uncertainty in the measurements. In addition,

the jet energy resolution of sampling calorimeters also depends on response

differences between electromagnetic and hadronic particles. Since the energies

of all hadrons (both neutral and charged) are not known a priori, it is not

straightforward to distinguish the sources of energy and to properly compensate

for differences in response. The response differences can therefore introduce

disparity in the energy measurements of jets with the same energy [10].

Discovery of the Higgs boson will require excellent jet energy and shape

resolution since Higgs decay channels often involve multi-jet final states. For

example, the interaction bbjjhZee →→ results in a four hadronic jet final state.

The discovery of the Higgs and the physics beyond the Standard Model

will very likely create signals in the hadronic calorimeter, and since hadronic

calorimeters have limitations with respect to the readout, it is desirable that High

17

Energy Physicists develop a timely solution that is “outside the box”. Currently

two ideas are under investigation.

2.7 Techniques to Improve Jet Energy Resolution

o Energy Flow (EF) Technique To improve the jet energy resolution of the calorimeter, the ALEPH

collaboration at LEP developed an “energy flow” (EF) technique, which takes

advantage of the low particle multiplicity in electron-positron ( +−ee ) collisions

[14]. The EF technique requires a precise tracking system that can measure the

trajectories and momenta of charged particles. The essence of the technique is

to associate a charged track with an energy cluster in the calorimeter and

replace the calorimeter energy with the better measured track momentum. The

energy clusters associated with tracks are then eliminated from the calorimeter

energy sums. The remaining energy is associated with the energy deposited by

neutral particles. Since typically the momenta measured by tracking systems

are of higher precision than the energy measurement from calorimeters, and on

average about 2/3 of hadronic jet energy is carried by charged particles, this

technique naturally improves jet energy resolution.

The EF method requires high calorimeter granularity to isolate tracks

associated with energy clusters. The tracking volume must be large or have a

strong magnetic field to permit spatial separation of particles at the calorimeter.

18

Given the energy regime of a future linear collider, it is necessary to cover a

large volume, resulting in a significant increase in the number of readout

channels. Due to the cost of the readout system, the overall price of a hadronic

calorimeter compatible with the EF technique is likely to be expensive using

conventional analog readout.

o Digital Hadronic Calorimetry Digital Calorimetry coupled with the EF technique provides a means of

achieving sufficient energy resolution while maintaining reasonable cost. In

contrast to analog Calorimetry, in which the energy deposited in each cell is

represented by a real number, digital Calorimetry simply registers energy

deposition above a threshold in each cell as a single bit. The threshold must be

low enough to efficiently register a minimum ionizing particle (MIP). The energy

deposited in a given layer of a digital calorimeter can be mapped as a two-

dimensional array of cells, with each cell represented by a single bit that is “on”

if the energy is above the threshold and “off” otherwise. The overall energy can

be estimated from the number of “on” cells and from other strongly correlated

characteristics of the shower such as longitudinal or transverse profile.

The digital technique is better suited to hadronic rather than

electromagnetic Calorimetry since hadronic showers are large enough to allow

for cell sizes that are not impractically small.

19

The next chapter introduces the GEM detector, its basic geometry and

principles of operation, etc.

20

CHAPTER 3

Gas Electron Multiplier (GEM) as a Drift Chamber

3.1 Introduction Charged particles can be detected in drift chambers because they ionize

the gas along their flight paths. The energy required for them to do this is taken

from their kinetic energy and is very small, typically a few keV per centimeter of

gas under normal conditions [15].

The ionization electrons of every track segment drift through the gas and

are amplified at the wires in avalanches. Electrical signals that contain

information about the original location and ionization density of the segment are

recorded.

The behavior of the drift chamber depends crucially on the drift of the

electrons and ions that are created either by the particles measured or in the

avalanches at the electrodes. In addition to the electric field, there is often a

magnetic field, which is necessary for particle momenta measurements.

21

3.2 GEM Detector and its Role

Using contemporary high-density readout electronics, a proportional gain

of several thousand is required for fully efficient detection of minimum ionizing

particles in thin layers of gas, typically limited to two or three millimeters in order

to minimize drift time. GEM technology meets this challenge [16,17,18,19].

GEM was developed as a way of boosting the performance of microstrip

gas chambers. Increasing the amplification in a microstrip gas chamber to

achieve a bigger signal means increasing the operating voltage, but this cannot

be continued indefinitely. Reasons for this include:

1. Charged particles lose energy when they ionize atoms. The energy lost

to ionize an atom by charged particles decreases with the energy of the

charged particles.

2. High energy “minimum ionizing” particles produce relatively small

numbers of electrons. High gains are needed to detect these signals.

3. Increasing the voltage increases the gains and at higher gains, collision

by-products such as heavy, slower particles can release substantial

additional ionization, resulting in a discharge, which could ruin delicate

instrumentation [20].

A very attractive and promising solution to overcome these issues is to

separate the amplification stage of the microstructure detector from the charge

collection structure. This can be elegantly achieved using a pre-amplification foil

such as gas electron multipliers.

22

3.3 Basic Structure

A GEM consists of a Kapton mesh typically 50 µm thick coated with 5 µm

of copper on both sides of the Kapton as shown in Fig. 3.1. Holes in the mesh

are conical in shape, typically 100 µm wide at the metal level and 40-80 µm

wide in the middle of the insulator; with a pitch of 140 µm. Application of a

suitably large voltage difference between the metal layers of the GEM produces

an electric field in the holes sufficient for gas multiplication.

Figure 3.1: GEM with XY readout [21]

23

Figure 3.2: Schematic view of a GEM detector. The drift space is 3 mm and the induction gap is 1 mm thick [22].

The basic detector is shown schematically in Fig 3.2. It consists of an

upper electrode, delimiting a three mm thick conversion and drift region, one

GEM amplifying mesh, and an induction gap one mm thick terminating with a

printed circuit board with parallel pick-up strips 150 µm wide at 200 µm pitch.

The GEM meshes are manufactured on metal clad Kapton foils 100 µm thick,

etched with a high density of holes (typically 120 µm in diameter at 200 µm

pitch) using the photo-lithographic process described in the appendix C.

3.4 Formation of Avalanche in GEM

By applying a potential difference between the two copper sides, an

electric field as high as 100 kV/cm is produced in the holes which acts as a

charge multiplier for electrons released in the gas.

24

Figure 3.3: The electric field in a GEM microhole [21].

Several GEM foils can be used in cascade, increasing the overall gain; a

patterned charge-collection anode permits the detection and localization of the

primary ionization. The number of electrons, n, in the avalanche grows

exponentially [23]: )(

0xenn α=

where n0 is the number of primary electrons, x is the unit path length and α is

the probability of ionization per unit length. The multiplication factor A in a

uniform electric field is eαx. α depends on the nature of gas and its density. If

the electric field is not uniform, α is a function of the path x and the

multiplication factor gain is

25

∫=2

1)(

r

rdxx

eAα

This is the gas gain of the GEM. When one electron enters a hole in the GEM a

maximum of about 410 electrons can exit on the other side.

3.5 Discharge and Breakdowns in GEM

It has been observed, however, that when operating the detectors at high

gain, exposure to high radiation fluxes or the release of a large amount of

charge in the sensitive volume may induce a breakdown of the gas rigidity.

It was discovered that for all planar detectors, at low rates, discharges

appear at a critical total charge in the avalanche, maxQ such that:

max0 QAn ≥

A is the gas gain and n0 is the number of primary electrons which initiated

the avalanche. When An0 is equal to maxQ there will be a discharge. It follows

from this equation that the maximum achievable gain for soft x-rays will be very

different from that of heavy ionizing particles. For GEM the total gain limit maxQ

is around 107 electrons/avalanche, and this limit can be reached when several

GEMs are put in succession. For soft x-rays (60 keV) n0 is typically 103 and this

gives a gain A of 104. But for heavy ionizing particles, for example alpha

particles, n0 is typically 105 and this gives a allowed gain of only 102.

The discharge limit is dependent on the gap distance in the gas

chamber. For most gaseous chambers the limit in electrons per avalanche, Q,

26

is 108, but for GEMs this limit is lower because of a very small gap between the

anode and cathode.

3.6 GEM in Various Combinations

3.6.1 Single GEM Operation

A single GEM detector [24] consists of a conversion and drift region, a

GEM foil, an induction region and a printed circuit board (PCB) for electron

collection. Typical thickness values for fast beam detectors are three mm and

one mm for the drift and induction gaps, respectively. An essential feature of the

device (not found in any other gas detector) is that the charge multiplication

electrode, receiving the high voltage (the GEM) is electrically separated from

the readout board. The readout can be patterned at will with strips or pads.

Figure 3.4 shows a single GEM configuration.

Figure 3.4: A schematic diagram of a single GEM.

Proportional avalanche amplification has been observed in a wide range of

gases and pressures. The effective gain of the structure, defined as the ratio of

collected to primary charge, can reach 104.

27

3.6.2 GEM+MSGC (Micro-strip Gas Chamber)

The GEM electrode can be used as charge pre-amplifier in front of another

gas amplification device, as for example a micro-strip chamber [24].

Figure 3.5: Single GEM with MSGC.

Combining the two elements, one can obtain much larger overall gains or,

conversely, operate the structure at lower (and safer) voltages for each of the

two amplifiers. This greatly increases the reliability of the detector, a solution

adopted for the tracker of the HERA-B experiment.

This first approach to solve the discharge problem is largely superseded

by the further work on multiple GEM structures.

3.6.3 Double GEM Detector

A GEM can be used as charge preamplifier to a second GEM [24]. The

double GEM (DGEM) detector has a drift, a transfer and a signal induction

region [Fig. 3.6]. The total effective gain of the DGEM is roughly the product of

the gains of the two GEMs.

28

Figure 3.6: A schematic diagram of a double GEM detector

3.6.4 Triple GEM Detector

A cascade of three GEMs permits the detector to reach even higher gains,

particularly in the presence of heavily ionizing backgrounds [24]. Multiple GEM

devices allow one to obtain very high gains in pure noble gases.

Figure 3.7: Triple GEM detector

3.7 Advantages of GEM

v The signals are purely due to electrons, without ion tails, and are therefore

very fast [25].

29

v Good position resolution, ~ 40 µm.

v Time resolution of ~ 5 nanoseconds.

v Gains up to ~104.

v Can operate in high rate and harsh experimental conditions

v Can be used as charge preamplifiers, in combination with micro-strip gas

chambers (MSGCs)

v Using multi-layer boards, all coordinates can be kept at ground potential,

resulting in a considerable simplification in the read-out electronics.

v GEM devices are robust and easy to manufacture.

v Proportional amplification and charge detection are performed on separate

electrodes. Advantages of de-coupling of amplification and readout are:

v With proper choice of the operating conditions, one can effectively

avoid the propagation of accidental discharges to the sensitive

electronics.

v The structure of the readout plane itself can be easily adapted to the

experimental needs, with pads or strips of arbitrary shapes.

30

Chapter 4

Monte Carlo Tools

4.1 Introduction

Detailed understanding of shower development and its dependence on the

energy and nature of the showering particles and on the materials in which the

processes take place, are crucial in the design of calorimeter systems for

particle physics experiments. Analytical study of the average shower behavior is

in general not sufficient for this purpose, since the most critical aspects of the

system’s performance are dictated by event-by-event fluctuations in the

absorption processes. For this reason, the simulation of shower development

processes by means of Monte Carlo techniques has been developed [10].

In these simulations, models for the elementary electromagnetic and

hadronic processes are employed to generate individual cascades and to follow

their development in considerable detail.

31

The reliability of these simulations depends on the quality and

completeness of the models used to describe the underlying physics processes.

The physics processes that govern the electromagnetic shower development

are studied in detail and found to be generally simpler than the physical

processes that are responsible for hadronic shower development.

For hadronic showers, particle production is the most straightforward

phase of the shower development, but the nuclear sector is considered more

complicated to describe because of the enormous variety of processes that may

occur. Hence the Monte Carlo packages, for example, GEANT-based packages,

are not very reliable as far as hadronic Calorimetry is concerned.

4.1.1 Conclusions Based on the Results of Simulation Packages:

When testing these programs and comparing the results with

experimental data, one should also realize that some types of data are much

more sensitive to the correct implementation of the physics than others. For

example, a certain simulation program may do a good job in reproducing

experimentally observed shower profiles, but at the same time fall short in the

area of energy resolutions. The reason is that energy resolution depends on the

event-by-event fluctuations and the correct implementation of the physics

processes governing the absorption of hadrons in dense matter.

32

In general, one should be careful with conclusions about the validity of

predictions from such simulation programs.

4.2 GEANT4 – Detector Simulation Program

GEANT4 (GEometry ANd Tracking) is a toolkit for the simulation of the

passage of particles through matter [26]. Its areas of application include high-

energy physics and nuclear physics experiments, medical, accelerator and

space physics studies. GEANT4 provides a complete set of tools for all aspects

of detector simulation:

• Geometry

• Tracking

• Detector Response

• Run, Event and Track management

• Visualization

• User Interface

An abundant set of physics processes handle the diverse interactions of

particles with matter across a wide energy range, as required by the GEANT4

multidisciplinary nature; for many physics processes a choice of different

models is available. The toolkit includes:

• Random number generators

33

• Physics units and constants

• Particle Data Group compliant particle management

• Interfaces to event generators and to ODBMS (Object-oriented

database management system)

The GEANT4 Object Oriented design allows the user to understand,

customize or extend the toolkit in all the domains. At the same time, the

modular architecture of GEANT4 allows the user to load and use only the

components needed.

4.3 Mokka – Detector Simulation Program

Mokka is a full simulation [27] using GEANT4 and a realistic description of

a detector for the future linear collider. The basic model, proposed for the

TESLA project, is described in the TESLA Technical Design Report (T.D.R)

Since 1999 several new detector parts, models and prototypes became

available in the Mokka geometry database. For my research, I am using Mokka

TDR model.

4.3.1 Description of Mokka TDR model

Mokka TDR (TESLA Technical Design Report) consist of:

Ø Electromagnetic calorimeter.

Ø The hadronic calorimeter.

34

Ø 4 Tesla field in all the detector room

Figure 4.1 shows the schematic view of TESLA detector. Dotted red lines

are the X-axis and Y-axis. Z-axis (beam line) is pointed towards the intersection

of the X-axis and Y-axis. The first layer of detector around the beam line is

ECAL. HCAL is the next and the magnetic coils surround the HCAL.

Figure 4.1: Primary detector dimensions. Green shows ECAL, yellow is HCAL and blue is the structure containing the magnetic coils.

35

4.3.2 Electromagnetic Calorimeter

The simulated electromagnetic calorimeter for TESLA is formed from of a

barrel closed at each end by an end-cap. The barrel is divided into eight staves,

with each stave divided into five modules [see Fig. 4.2]. Each module is placed

1700 mm from the beam axis (Z) and contains forty layers of W/G10/Si/G10

plates. Each layer within the module is divided into a number of cells, and each

cell is assigned two integer numbers I and J. The layer itself, within the module,

is assigned a number K.

Barrel: For all layers the Si plate is 0.5 mm thick and is embedded in two

G10 plates of 0.8 mm each. For the first 30 layers the W is 1.4 mm thick and for

the last 10, 4.2 mm. ECAL hits are collected only in the Si plates, in cells of 11×

cm2.

Figure 4.2: The ECAL has eight staves and each stave contains five modules.

36

End-Cap: Each end-cap has 4 modules and each module has the same

layer structure and thickness as for the barrel, but the plates are perpendicular

to the Z-axis. The end-caps are placed 2800 mm away from the detector

collision point.

4.3.3 Hadronic Calorimeter

The HCAL is formed from a barrel surrounding the ECAL, closed on each

end by an end-cap. Like the ECAL, the barrel of the HCAL is also divided into 8

staves, with each stave divided into 5 modules. Figure 4.3 shows TDR HCAL

layers. Each module has 40 layers, with each layer consisting of plates of 18

mm of Fe and 6.5 mm of polystyrene scintillator (shown in green in Fig. 4.3).

HCAL hits are collected in polystyrene scintillator, in cells of 11× cm2.

4.3.4 Generation of Primary Events

Mokka has two methods for event generation: particleGun and Pythia.

Ø /generator/generator <HEPEvt file>

HEPEvt file is the name of a Pythia event file of users choice.

Ø /generator/generator particleGun

This command enables the GEANT4 default gun machine.

Appendix A lists the macro file used for the event generation.

4.4 Mokka GEM

The sensitive material in the Mokka TDR is polystyrene scintillator, but in

the Mokka GEM, we replace it with GEM detector.

37

Figure 4.3: Mokka TDR – sensitive layers in hadron calorimeter

Venkat, a HEP graduate student, initially implemented a double GEM

geometry, followed by a simpler geometry (see Fig. 4.4). The motivation for a

simpler geometry is that it took 25.2 seconds to run a single event for the simple

geometry vs. 43.7 seconds per event for the detailed geometry. From Fig. 4.5,

it is seen that the results from a gaussian fit to the Mean Energy <E> are

approximately the same for both techniques.

1 / 9 / 2 0 0 3 U T A -G E M S i m u l a t i o n R e p o r tV e n k a t e s h K a u s h i k

9

D o u b l e G E M G e o m e t r y

0 . 0 051

. 0

C uK a p t o n

A r C O 2

G 1 0

0 . 0 05

6 . 5 m m S i m p l e G E M

3 . 4 m m A r C O 2

G E M3 . 1 m m

D e t a i l e d G E M

• S i m p l e G E M u s e s a v e r a g e d e n s i t y

Figure 4.4: Simple GEM and detailed GEM. Courtesy of Venkat

38

Figure 4.5: Energy distribution for 75 GeV pions using detailed geometry (blue) and simple geometry (magenta)

Figure 4.6: Gain at 420=∆V Volts for a Double GEM [28]

<E>=0.80 ± 0.007MeV <E>=0.81 ± 0.008MeV

39

GEM Group at UTA HEP (high-energy physics) is operating double GEM

at the potential difference of 420.0 Volts and at which value, consulting the Fig.

4.6; gain comes out to be 3500.

4.5 ROOT for Analysis

ROOT is a C++ framework [29] developed since 1994 at CERN. The

ROOT system consists of a huge C++ library with all the functionality needed to

handle and analyze large amounts of data in a very efficient way. Included in

the ROOT system are histogramming methods in one, two and three

dimensions, curve fitting, function evaluation, and graphics and visualization

classes.

CINT C++ interpreter is aimed at processing C/C++ scripts. Scripts are

programs performing specific tasks. I am using ROOT as a display

development tool and the ROOT interpreter as a scripting language for

interactive analysis and displays. The advantages are the freely configurable

graphs and displays.

Further documentation on ROOT and GEANT4 is available on the web.

In the next chapter, I will describe how these tools were used in the simulation

of GEM in Mokka.

40

CHAPTER 5

SINGLE PARTICLE STUDY RESULTS

5.1 Analog Studies Using Mokka TDR

For simplification, I started my studies with single pions interacting in the

TESLA TDR detector. For event generation, the particleGun command in

Mokka was used. Mokka offers two options for the generation of events –

particleGun and a Pythia generated HEPEvt file. Table 5.1 lists the commands,

in a script file, used to generate events for 3 GeV pions.

Table 5.1: Example of Mokka script file /generator/generator particleGun

/gun/position 0 0 0 mm /gun/direction 0 1 0

/gun/energy 3.0 GeV /gun/particle pi-

/run/beamOn 5000

Command line to run the script file

./Mokka.TDR –o PionTDR/3GeV –m macro3

41

For a list of all command line arguments, see appendix A. For ECAL and

HCAL, Mokka creates a hits file for each event. Once the output files [see the

excerpts from the sample files in appendix A] were obtained, programs were

developed in C/C++ to analyze the data and ROOT was employed to display

the results. Programs are listed in Appendix B. Steps in the analysis:

1) Typically 5000-15000 single pion events were generated with energies of

5, 10, 25, 50, 75 and 100 GeV.

2) Define EEM to be the energy deposited in ECAL, EHC the energy

deposited in the HCAL. Then TotalE is the total energy such that

HCALECALTotal E E E += . The distribution of total visible energy TotalE was

plotted and fitted using a gaussian fit for each incident pion energy. The

mean energy >< E from the gaussian fit was plotted against each

incident energy Eπ. A gaussian fit has three parameters: constant, mean

(µ) and standard deviation (σ) [see appendix for details]. Root also

calculates the statistical error in the parameters. An example is shown in

Fig. 5.1 for 50 GeV pions; the mean live energy >< E is 1818 ± 6.24

MeV and σ is 408.6 ± 4.39 MeV.

3) Systematic errors in the mean and sigma from the gaussian fit of the

data were determined by plotting two histograms. One was fitted using

the range (0,XMax) where XMax is the maximum in the data set [Table A-

2a] and the other using range ),( 21 xx where x1 and x2 are energy values

which give a better 2χ fit compared to the first method [Table A-2b]. The

difference between the means from the two fits gives the systematic

error in the mean.

42

4) From the data collected in step 2, the response curve (Fig. 5.2) was

plotted. The slope of the line defines the calorimeter response. The

response R± εstatistical for the Mokka TDR was calculated to be 0.03745

± 0.0003772. Goodness of fit can be expressed in terms of 2χ and the

number of degree of freedom - 4/547.4/2 =dofχ . From the response

curve it is seen that the calorimeter is linear, that is, the energy deposited

is directly proportional to the energy of the incident particles.

5) Energy deposited in the calorimeter was converted to account for the

response, using REEC /= . The converted energies were plotted and the

histograms were fitted using a gaussian fit [Fig. 5.3].

6) Systematic errors were calculated for the sigma and mean values using

the strategy detailed in step 3.

7) To determine the resolution of the detector, the mean energy >< E and

sigma σ for each pion sample were noted. For 50 GeV pions, for

example, the mean energy >< E = 48.7± 0.1839 GeV and sigma σ =

10.71± 0.1089 GeV. The data thus acquired were plotted to generate the

resolution curve, >< E/σ vs. >< E (Fig. 5.4). As mentioned in Chapter

2 section 2.5.3, resolution for a linear calorimeter can be described as

EaEE // =σ , but not all types of fluctuations contribute to the

resolution as E/1 . Some fluctuations are energy independent, e.g.,

fluctuations resulting from non-uniformities in the calorimeter structure.

Fluctuations resulting from electronics noise are 1/E dependent. In our

study resolution is represented by the equation:

43

%%%/ c

Eb

Ea

E ++><

>=<σ .

The value of a% (resolution) represents the contributions from sampling

fluctuations, while c% (constant term) represents instrumental effects that tend

to dominate at high energy where the effects from gaussian fluctuations are

small. The noise term is represented by b%. For our study we have neglected

the noise term, setting b = 0 because there is no electronic noise in the Monte

Carlo simulation. Since electronics noise and stochastic errors are not

correlated, the errors can be added in quadrature.

Figure 5.1 Total live energy distribution for 50 GeV pions in the Mokka TDR with the result of a gaussian fit to the data.

44

Figure 5.2: Mokka TDR response curve fitted with a linear function.

Figure 5.3: Converted energy distribution for 50 GeV pions in the Mokka TDR.

45

Figure 5.4: Resolution curve for single pion detection of Mokka TDR with systematic errors [Table G-2b in appendix G].

The resolution of Mokka TDR is described by the equation:

)%2898.061.17()%385.11.30(

/ ±+><

±>=<

EEσ

The resolution improves with increasing energy; for example, the resolution is

27.5% for 10 GeV pions and 21.5% for 75 GeV pions. This is one of the

attractive features of calorimeters. The instrumental effects represented by c =

17.61% become important at higher energies.

5.1.1 Systematic Errors and Their Effects on the Fit

The distributions in Fig. 5.1 and 5.3 are only approximately gaussian,

and using a gaussian fit introduces errors. Similarly bin size and the range of

46

the fit introduce uncertainty. All these contribute to the total systematic error,

and since it is difficult to estimate the systematic error, resolution graphs were

plotted using the systematic error that was calculated from the experimental

data [Fig. 5.4], and also using twice the calculated error [Fig. 5.6] to

compensate for other possible systematic uncertainties in this analysis. The

value of dof/2χ improved from 34.3/4 to 8.6/4 when the larger error was used

but the resolution and the constant term remained unchanged.

Figure 5.5: Resolution curve for single pions using the Mokka TDR with systematic errors multiplied by two.

The value of a% (resolution), approximately 30%, was very encouraging

because it is consistent with the result obtained in a similar analysis [30,31].

47

After the successful testing of the tools on the Mokka TDR calorimeter, the next

step was to employ the tools on a Mokka GEM-based calorimeter.

5.2 Analog Studies Using Mokka GEM

Mokka GEM, as mentioned in Chapter 4, substitutes GEM structures in

the sensitive layers instead of polystyrene scintillator, which is used in the

Mokka TDR. ECAL is the same in both Mokka GEM and Mokka TDR.

Gain of GEM Detector:

The gain G of the GEM detector, as noted in section 4.4, is 3500.

Difference of Responses Between Hadronic and Electromagnetic

Calorimeters: The calorimeter response to hadrons is smaller compared to electrons of

the same energy. The factors behind this include:

v Due to differences in ECAL and HCAL technology, one gets different

responses in the two calorimeters. For example, the sensitive material in

ECAL is silicon, while the sensitive material in the HCAL is polystyrene

scintillator. Similarly, the passive material in the ECAL is tungsten while

it is stainless steel in the HCAL [See Chapter 4 - Electromagnetic

Calorimeter (section 4.3.2) and Hadronic Calorimeter (section 4.3.3) for

additional details].

v In the absorption of hadronic showers, a significant fraction of the energy

is invisible, that is, it does not contribute to the calorimeter signal. The

primary sources of invisible energy are:

48

1) Energy used to release nucleons from nuclei, and

2) Neutrinos and muons do not typically deposit significant amounts of

energy in the detector and hence contribute to the missing energy

[See Fig. 2.2].

The following figures clearly differentiate the response of hadronic and

electromagnetic calorimeters. Plots A and B in Fig. 5.6 show the energy

distributions in ECAL and HCAL, respectively. Plot A includes only those events

in which at least 85% of the total energy was deposited in ECAL. Similarly, plot

B is for events in which at least 85% of the total energy was deposited in HCAL

[Table 5.2]. Events that did not satisfy these criteria are shown in plot C, and

plot D includes all events. Plot D shows two distinct peaks representing the

ECAL and HCAL signals, respectively, instead of a single gaussian peak as in

Fig. 5.1.

Table 5.2: Strategy for selecting events for ECAL and HCAL EECAL/ETOTAL≥0.85 ECAL Event – Plot A

EHCAL/ETOTAL≥0.85 HCAL Event – Plot B

EECAL/ETOTAL<0.85 and EHCAL/ETOTAL<0.85 Remaining – Plot C

HCALECALTotal E *G E E += Total – Plot D

49

Figure 5.6: Plot A) is the ECAL signal, B) is the HCAL signal. Plot C) shows the energy distribution for events that did not fall into either the ECAL or HCAL plot.

Plot D) shows the total signal for 10 GeV pions.

To take into account the difference in responses of the hadronic and

electromagnetic sections of the calorimeter, I calculated a weighting factor

using the following steps:

1) Pions of various energies [5,10,20,50,75,100 GeV] were incident upon

the Mokka GEM calorimeter, and the total live energy was reconstructed as

HCALECALTotal E *G E E += , where EECAL is the energy deposited in ECAL, EHCAL is

the energy deposited in the HCAL and G is the intrinsic gain of the GEM

A) FEM>=0.85 B) FHC>=0.85

C) Remaining D) Total

50

detector. To obtain ECAL and HCAL dominant signals, only those events with ≥

85% of the energy deposited in either the ECAL or HCAL were accepted. Then

I plotted the visible energy distributions in the ECAL and HCAL, fitted the

resulting curves and then noted down the fit parameters. Using the data thus

obtained, response curves were plotted for ECAL and HCAL.

Figure 5.7: Energy distributions in the ECAL and HCAL for 50 GeV pions.

2) As seen in Fig. 5.9 the higher the incident energy of the pions the

higher the energy that is deposited in the HCAL compared to the energy

deposited in the ECAL. This difference, combined with the asymmetric

fluctuations in the energy sharing between the two calorimeters, led to the fact

that two distinct gaussians instead of one characterize the distribution [See Fig.

51

5.7]. A weighting factor W was introduced to scale the hadronic response,

thereby resulting in a single gaussian distribution.

3) Different values of the weighting factor W, ranging from 0.18 to 0.285,

were scanned to observe the effect in the energy distributions for different

energy pions. The value of W = 0.22 was selected from the range because it

gave approximately normalized distributions for the different pion energies.

4) Finally as a check, the weighting factor W was determined by plotting

ECAL and HCAL response curves [Fig. 5.9]. Let ECALS be the slope of the ECAL

response curve, HCALS the slope of HCAL response curve, then W (the relative

weighting factor between ECAL and HCAL) is calculated using the formula

HCALECAL SSW /= . W was determined to be 0.285± 0.077.1

Since the number of events in ECAL histogram is only six for 50 GeV

pions [top of Fig. 5.8] and three for 75 GeV pions [bottom of Fig. 5.8], it was

difficult to apply a gaussian fit, and thus for the calculation of the weighting

factor we decided to limit the range of the fit from 0 to 20 GeV [see Fig. 5.9].

1 Since the sensitive materials in the Mokka TDR for ECAL and HCAL are

silicon and polystyrene scintillator, respectively, it was expected that the

differences of responses of ECAL and HCAL in Mokka TDR would call for

compensation. The weighting factor for Mokka TDR was determined to be

0.569±0.011 [Fig. D.1 in appendix D]

52

Figure 5.8: Signal distribution for showers induced by 50 and 75 GeV pions in the ECAL, respectively. Fit to the data is gaussian.

53

Figure 5.9: Calculation of the weighting factor. Top plot shows the response of ECAL and the bottom is the response curve for HCAL.

5) The total energy is now calculated using HCALECALTotal E*G* W E E += .

Energy distributions were plotted for each incident-pion-energies. The energy

distribution for 50 GeV pions is shown in Fig. 5.10.

54

Figure 5.10: Total live energy distributions for 50 GeV pions after taking into account the difference in HCAL and ECAL responses with two different ranges

for a gaussian fit.

55

6) Then I followed steps 2-7 outlined for Mokka TDR studies. Plots for

response, converted energy distribution and resolution curve are shown in Figs.

5.11-5.13. The response is found to be 0.02612 ± 5.99e-4. The resolution of

the detector [Fig. 5.13] can be represented by:

)%800.094.19()%15.583.39(

/ ±+><

±>=<

EEσ

The curve drawn through the experimental data points do not extrapolate to the

bottom right corner of the graph, but instead to a resolution of 19.94% at infinite

energy.

Figure 5.11: Response curve for Mokka GEM.

56

Figure 5.12: Total converted energy distributions for 50 GeV pions. Two different ranges for a gaussian fit are shown.

57

Figure 5.13: Resolution curve for Mokka GEM [Table G-5b in appendix G].

5.3 Mokka GEM Digital Analysis

5.3.1 Feasibility of Digital Use of GEM To study the feasibility of a digital approach using the GEM, pions were

incident upon the HCAL directly, using the command

The purpose of the study was to plot the mean number of cells hit vs. incident

pion energies to validate the approach of a digital calorimeter. The digital

strategy is similar to the analog strategy except that instead of taking <EHCAL>

(mean energy deposited in the HCAL), the mean number of cells hit in HCAL

<NHCAL> is used to calculate the total energy deposited in the calorimeter.

Figure 5.14 shows the relationship between <NHCAL> vs. incident pion

energy. Two fits, to the distribution of cell multiplicity vs. energy were tested, a

./Mokka.GEM –S hcalferpc1 –o HcalOnly/10GeV –m macro10

58

linear fit [top plot in Fig. 5.14] and a quadratic fit [bottom plot in Fig. 5.14]. The

quadratic fit gives the best χ2 fit. The relationship between <NHCAL> vs. incident

pion energy (Eπ) makes it possible to calculate the energy of the particles if the

mean number of cells hit is known. This suggests that a digital method of

calorimetry using GEM is not only feasible but also economical, because

instead of reading out the energy deposited in a cell, which is a real number

comprised of 12 bits, a digital approach requires only one bit – 0 or 1. Zero

means the energy deposited was below some threshold value and one means

that energy deposited was above the threshold. Digital study comprises of

counting the number of cells with energy deposited above threshold and

applying the relationship to calculate the energy of the incident particles.

Figure 5.14: Mean numbers of cells hit vs. incident pion energy.

59

The number of cells hit per event was plotted as a function of energy

deposited in HCAL per event in Fig. 5.15. This plot includes all incident pion

energies.

Figure 5.15: Number of cells hit vs. energy deposited in the HCAL only.

5.3.1.1 Plateau Effect and Cell Occupancy A gradual plateau at increasing live energies (EHCAL>2 GeV) can be seen

in Fig. 5.15. The reason is that at higher energies the number of cells hits is not

directly proportional to the energy deposited, but instead reaches a constant

value. A given detector has a fixed number of cells in the active medium, and at

higher energies some of the cells are hit more than once, as indicated in Figs.

60

5.16-5.17. For 100 GeV pions, 20% of cells were hit twice, while for 3 GeV only

10% were hit twice. The number of cells with multiple hits increases with

increasing energy.

Figure 5.16: Cell occupancy for 3 GeV pions in Mokka GEM.

61

Figure 5.17: Cell occupancy for 100 GeV pions in Mokka GEM.

Steps of Digital Analysis: 1) First step in the digital analysis is the determination of dNdE / , where E

is the energy deposited in a cell and N is the number of cells. The total

deposited energy is then calculated using dNdENEE ECALTOTAL /∗+= .

ETOTAL is the total visible energy deposited per event, EECAL is the energy

deposited in the ECAL per event and N is the number of cells hit in the

HCAL per event. A cell is counted as a hit when the energy deposited in

the cell is greater than or equal to the threshold. For the current study,

the threshold is set to be zero.

62

Figure 5.18: Relationship between energy deposited per event E vs. numbers of cells hit per event N. The top plot is the profile histogram of the

bottom 2-d histogram .

From Fig. 5.18 it is seen that the linear fit has 95/12490/2 =dofχ while,

for the quadratic fit it is 1327/94. Hence a quadratic fit better describes the data

compared to the linear fit. Using the quadratic fit the total energy is represented

by )**( 2210 NpNppEE ECALTOTAL +++= . For the linear fit the total energy is

represented by )*( 10 NppEE ECALTOTAL ++= , where p0 is the y-intercept and p1

is the slope of the straight line ( bmxy += ).

63

2) The total signal was divided into ECAL and HCAL samples using the

strategy described in the analog study. If EECAL/ ETOTAL ≥ 0.85 the event

belongs to ECAL, if EHCAL/ ETOTAL ≥ 0.85 the event is filled in the HCAL

histogram.

3) Responses were plotted for the ECAL and HCAL, and the relative

weighting factor was calculated which was then used to compensate the

response differences between the two detectors. The total energy is

plotted for each incident pion energy using

dE/dN*N*WEE ECALTOTAL += .

Figure 5.19: Weighting factor – digital study for Mokka GEM. The top plot shows the response curve for ECAL, while the bottom plot shows the response

curve for HCAL.

64

Figure 5.20: Response curve for digital study – Mokka GEM

4) Same as steps 3-7 described in the Mokka TDR study [section 5.1].

Plots for weighting factor, response and resolution are shown in Figs.

5.19-5.21. The response curve [Fig. 5.20] shows a linear fit. Hence a

50 GeV pion deposits 1.1 GeV while a 20 GeV pion deposits only 0.45

GeV. The resolution of the Mokka GEM calorimeter is represented by

)%926.027.5()%33.585.58(

/ ±+><

±>=<

EEσ .

65

Figure 5.21: Resolution curve – digital study for Mokka GEM.

5.4 Muon Study

Muons are minimum ionizing particles (MIP) and for digital study, I wanted

to select the threshold which when applied to the data will retain 95% of the MIP

information [Fig. 5.22]. For the Mokka GEM, the threshold was determined to be

0.230 MeV. The purpose of applying a threshold is to optimize the digital study.

Applying a threshold decreases the readout cost while keeping only the data

that is above noise and background. Since the discovery of Higgs will involve

backgrounds from known physics processes, it is important to apply the

threshold cut judiciously. The efficiency plot in Fig. 5.23 relates the efficiency to

the threshold applied for Mokka GEM.

66

Figure 5.22: Determination of threshold from the cell energy distribution of muons in HCAL of Mokka GEM.

67

Figure 5.23: Correlation between efficiency and threshold for 100 GeV muons in HCAL of Mokka GEM.

5.5 Effect of Threshold cut on the Response and Resolution of the

Calorimeter

The introduction of a threshold cut improves the resolution compared to

the resolution without the threshold; compare Figs. 5.27 and 5.21. The

resolution improves from 56.85% to 52.46%. The strategy adopted is analogous

to the one applied for the digital study, except that a cell is considered to be hit

only if the energy deposited is above the threshold cut. Plots for energy

68

deposited per event vs. number of cells hit per event (E vs. N), determination of

weighting factor, response and resolution curves are shown in Figs. 5.24-5.27.

As mentioned previously, the graph of E vs. N [Figs. 5.18 and 5.24] does

not exactly confirm to a linear fit. The χ2 for a polynomial fit of degree ≥ 2 is

better compared to the linear fit. The non-linearity was taken into account for

digital studies with a threshold cut and the results are plotted in appendix D.

The resolution of a digital of GEM detector with threshold is represented by

)%926.086.5()%86.546.52(

/ ±+><

±>=<

EEσ .

Figure 5.24: Calculation of dE/dN.

69

Figure 5.25: Weighting factor for Mokka GEM with threshold 0.23 MeV.

Figure 5.26: Response curve for Mokka GEM with threshold applied.

70

Figure 5.27: Resolution in Mokka GEM with threshold applied.

5.6 Leakage and its Effect on the Response and Resolution of the

Calorimeter

As the energy increases, the detector volume required to contain the

showers increases as well. If signals from the calorimeter are collected from a

given detector volume, then the fraction of the shower energy contained in that

volume decreases with increasing energy. This effect is known as leakage, and

it becomes more pronounced with increasing energy.

If we consider the worst case scenario in which all the particles that

deposit energy in the outer layer of the HCAL (number 40) escape, taking with

71

them the energy equal to the amount of energy that they deposited, even then

the fractional energy deposited is only around 1%. Figure 5.28 shows that in the

GEM calorimeter, leakage is less than 2.0 % of the total energy deposited. For

350 GeV pions (Fig. 5.29), the energy deposited in the outer layer is only 100

MeV and the fraction of hits for the outer layer is 3% of the total.

Figure 5.28: Fractional energy distribution in layer 40 in HCAL of Mokka

GEM.

Number of events in layer # 40=n40=1875 (Figure 5.30)

Number of events in all 40 layers=n=50992 (Figure 5.29)

72

Figure 5.29: Distribution of energy deposited in the 40 layers of HCAL.

Figure 5.30: Energy distribution (MeV) in layer number 40 in HCAL of Mokka GEM.

73

5.7 Energy and Number of Cells Hit Distribution

A study was performed to see a) if there is a punch-through effect in the

HCAL of Mokka GEM and b) to calculate the energy deposited in layer number

40 compared to energy deposited in all 40 layers to eliminate events that have

10% of the total energy deposited in the outer layers.

For each incident pion energy, 40 histograms were plotted, one for each

layer, along with the distributions of total live energy [Fig. 5.31] and the number

of cells hit in 40 layers [Fig. 5.32].

Figure 5.31: Energy distribution in 40 layers in HCAL of Mokka GEM.

74

Figure 5.32: Distribution of number of cells hit in 40 layers in HCAL of Mokka GEM.

75

CHAPTER 6

CONCLUSIONS

Tools were developed for analysis and tested on the Mokka TESLA TDR

detector for charged pions [30,31]. Afterwards, the tools were employed to

analyze a simulation of a Mokka GEM bases calorimeter for charged pions.

Two studies were carried out – analog and digital readout methods. The

resolution from the digital technique is somewhat worse compared to the analog

case, owing to the loss of information inherent to the digital readout. The digital

technique is useful only if utilized in tandem with an “Energy Flow” algorithm, on

which my colleague Venkatesh Kaushik is continuing the study.

The advantage of the digital technique is the application of threshold; a

threshold of 0.23 MeV was applied in order to reduce noise readout and to

gauge the effect of threshold. Application of the threshold results in improved

resolution, which is expected since a threshold cut decreases low energy tails,

thereby improving goodness of a guassian fit. The threshold study was

undertaken using two strategies - linear and nonlinear. As is seen from the plots

76

in Chapter 5 and appendix D, a nonlinear approach improves the resolution

because the dof/2χ of the nonlinear fit is better than to the linear fit.

In conclusion, the results are encouraging for future work. Remaining

tasks are to improve statistics, to develop improved techniques to compensate

for the differences in response of the hadronic and electromagnetic

calorimeters, determination of the number of electron-ion pairs generated

(partly done) for the study of GEM cell discharge probability, etc

Table 6.1: Compilation of fit parameters for response and energy resolution for TESLA TDR and GEM

Response visbEaE +=π Resolution:

b%E

a%E

+=σ

Detector Technology

Readout Method

aa δ± bb δ± aa δ± bb δ± TESLA-TDR Analog 0±1.31e-2 0.0375±3.77e-4 30.10±1.39 17.61±0.29

GEM Analog 0±1.26e-2 0.0216±5.99e-4 39.83±5.15 19.94±0.80 GEM Dig no

threshold 0±3.9e-3 0.0227±1.98e-4 56.85±5.33 5.27±0.93

GEM Dig. threshold=0.2

3MeV

0±3.2e-3 0.0231±1.7e-4 52.46±5.86 5.86±0.93

77

APPENDIX A

MOKKA

78

Launching Mokka:

To launch Mokka, without parameters, simply type

./Mokka

Command Line Parameters

o -?: summarize the line command parameters and exit

o -M <model name>: specifies the detector model to be simulated.

Default is TDR. Several models are available, for example, D08,

D09, D20 etc

o -S <sub detector> this option, if set, overrides the –M option. The

given model name is still valid concerning the world volume

dimensions, but just the <sub detector> given as parameter will be

build inside the world volume. Options available are ECAL, HCAL,

and TPC etc.

o -m <macro name>: specifies an initial macro file to be executed

before prompting for commands.

o -o <directory name>: specifies to run Mokka in “persistent mode”. It

means, the output event data files will be written in the given

<directory name>.If the directory does not exist, it will be created. If

the directory exists the program assumes “RESTART” mode in which

Mokka starts the simulation from the first event not yet done. If

<output directory> is not specified then Mokka runs in “transient

mode” which means that no data will be saved on the disk.

o -B <double>: This enables the user to apply an overall scaling factor

(0. to 1., defaults 1.) to the magnetic field map, if any.

79

o -t <double>: This new line command parameter specifies the TPC

primary energy cut in MeV. The default is 10 MeV to avoid TPC huge

output files. Setting it to zero enable users studding the TPC

particular readouts to save on disk all hits with more than the 2*Mips

threshold in the gas.

Example of Mokka Output ECAL file Table A.1: Sample of ECAL hits file

P M S I J K X Y Z E PID PDG 2 1 3 52 54 1 -171.8 1702.75 0 1.40E-01 1 -211 2 1 3 51 54 2 -177.9 1706.65 0 1.45E-01 1 -211 2 1 3 51 54 3 -174 1710.55 0 1.23E-01 1 -211 2 1 3 50 54 4 -180.1 1714.45 0 1.37E-01 1 -211 2 1 3 50 54 5 -176.2 1718.35 0 1.51E-01 1 -211 2 1 3 50 54 6 -172.3 1722.25 0 1.33E-01 1 -211 2 1 3 49 54 7 -178.4 1726.15 0 1.31E-01 1 -211 2 1 3 49 54 8 -174.5 1730.05 0 1.43E-01 1 -211 2 1 3 48 54 9 -180.6 1733.95 0 1.39E-01 1 -211

Table A.2: Sample of HCAL hits file

P M S I J K X Y Z E PID PDG 5 1 3 57 53 1 -220 1931.25 5 9.03E-01 1 -211 5 1 3 57 53 2 -230 1955.75 5 8.98E-01 1 -211 5 1 3 58 53 3 -230 1980.25 5 5.64E-01 1 -211 5 1 3 57 53 3 -240 1980.25 5 3.10E-01 1 -211 5 1 3 58 53 4 -240 2004.75 5 8.98E-01 1 -211 5 1 3 58 53 5 -250 2029.25 5 8.93E-01 1 -211 5 1 3 59 53 6 -250 2053.75 5 8.92E-01 1 -211 5 1 3 59 53 7 -260 2078.25 5 8.68E-01 1 -211 5 1 3 60 53 8 -260 2102.75 5 2.65E-01 1 -211 5 1 3 59 53 8 -270 2102.75 5 6.28E-01 1 -211 5 1 3 60 53 9 -270 2127.25 5 8.95E-01 1 -211

Mokka Output Format:

In persistent mode Mokka saves event data files in ASCII format

with the extension of hits in the directory specified in the command line

parameters. Event files are named as DDDDxxxxxx.hits

80

Where DDDD is the detector module (ecal, hcal, tpc…) and xxxxxx is the

event number. (Example ecal000000.hits, ecal000001.hits,etc)

Output format for Ecal and Hcal (Electromagnetic Calorimeter and

Hadronic Calorimeter)

The following format has been used for each hit in the calorimeter:

P S M I J K X Y Z E PID PDG

P = detector piece number:

1 = Ecal end cap –Z

2 = Ecal barrel

3 = Ecal end cap +Z

4 = Hcal end cap –Z

5 = Hcal barrel

6 = Hcal end cap +Z

S = stave number (1-8 for barrel, 1-4 for end caps)

M = module number in stave (1-5 for barrel, 1 for end caps). About the end

caps, 4 staves compose each end cap and each stave has one module.

I, J = the cell coordinates in the cells matrix (I, J>=0)

K = Sensitive (Si or scintillator) layer number (K>=1)

I, J, K is just the index inside the module. To address absolutely the cell

in the detector, all six values (P, S, M, I, J, K) have to be specified.

X, Y, Z = the cell center in world coordinates

E = the total energy deposited in the cell by the PID particle and its secondary

particles.

PID = primary particle id in the Phythia files

81

It means, several lines for the same (P, S, M, I, J, K) cell index could

exist in the same file if different primaries crossed the same cell. The total

energy deposited in a cell during an event is the total of all the lines with the

same cell index, indeed different PIDs and, for the same PID, different PDGs

82

APPENDIX B

PROGRAMS USED IN THE ANALYSIS

83

Description: Mokka Reader 1) Cell energy distribution 2) Number of cells hit per event distribution 3) Total live energy deposited per event distribution 4) Number of hits/cell distribution 5) Total energy deposited vs number of cells hit per event 6) Energy, deposited in outer layer #40, distribution 7) Layer number distribution per event 8) Number of cells hit per event distribution 9) Energy distribution in layers

// Latest work 05/28/2003 #include <stdio.h> #include <string.h> #include <stdlib.h> #define MaxLines 3000 #define Debug 0 #define Hcal_EndCap_negZ 4 #define Hcal_EndCap_plusZ 6 #define Hcal_Barrel 5 #define TL 40 //define total number of layers char *strapp( char *, char *); main( int ac, char **av) { // Variable declarations FILE *in, *out0,*out1,*out2,*out3,*out4,*out5,*out6,*out7,*out8,*out9; char *c; float GainFactor=3500; int t,j, num_events,CurrentFile=0, i = 0,cell_number=0,LinesPerEvent=0,n_above=0,result=0,ch=0; int P1[MaxLines],S1[MaxLines],M1[MaxLines],I1[MaxLines]; int J1[MaxLines],K1[MaxLines],Checked_Array[MaxLines]; double OLED=0.0; double e, energy,EnergyDepositedOuterLayer=0.0,Total_Energy,E_Array[MaxLines],Threshold=0.0,TotalEnergyPerEvent=0.0; double TotalEnergyAllEvents=0.0; char buf[8], *file; double MaxEnergy=0.0; int p,s,m,ii,jj,k,iCount=0; int L[TL]; //for layer data

84

double EndCap1[TL],EndCap2[TL],Barrel[TL]; // energy density int P_Min=1000,P_Max=0,Piece; // Some routine checks to read command line parameters right.. if( ac < 2) { printf("\nUsage : MR <type> <number of events> <GainFactor> <Threshold>\n"); exit(0); } num_events = atoi(av[2]); if( (out0 = fopen("CED.dat","w")) == NULL ) { printf("\nError opening the file %s\n","CED.dat"); exit(0); } if( (out1 = fopen("NCD.dat","w")) == NULL ) { printf("\nError opening the file %s\n","NCD.dat"); exit(0); } if( (out2 = fopen("DS.dat","w")) == NULL ) { printf("\nError opening the file %s\n","DS.dat"); exit(0); } if( (out3 = fopen("CO.dat","w")) == NULL ) { printf("\nError opening the file %s\n","CO.dat"); exit(0); } if( (out4 = fopen("TLED.dat","w")) == NULL ) { printf("\nError opening the file %s\n","TLED.dat"); exit(0); } if( (out5 = fopen("OLED.dat","w")) == NULL ) { printf("\nError opening the file %s\n","OLED.dat"); exit(0); } if( (out6 = fopen("OLED_Event.dat","w")) == NULL ) { printf("\nError opening the file %s\n","OLED_Event.dat"); exit(0); } if( (out7 = fopen("LDs.dat","w")) == NULL ) { printf("\nError opening the file %s\n","LDs.dat"); exit(0); } if( (out8 = fopen("LD.dat","w")) == NULL ) { printf("\nError opening the file %s\n","LD.dat");

85

exit(0); } if( (out9 = fopen("EnergyDensity.dat","w")) == NULL ) { printf("\nError opening the file %s\n","EnergyDensity.dat"); exit(0); } if(ac>=3 && atof(av[3])>0)GainFactor=atof(av[3]); if(ac>=4 && atof(av[4])>0)Threshold=atof(av[4]); c=strstr(av[1],"hcal"); if(c){ P_Min=4; P_Max=6; } else { P_Min=1; P_Max=3; } printf("GainFactor:%f Threshold:%f Number of arguments:%d Detector P_Min %d P_Max %d\n",GainFactor,Threshold,ac,P_Min,P_Max); ch=getchar(); while(CurrentFile < num_events) { //Looping over all events files.. sprintf(buf,"%06d",CurrentFile); file = strapp( strapp(av[1],buf),".hits"); //Create the string ecal0000xx.hits / hcal0000xx.hits if( (in = fopen(file,"r")) == NULL ) { printf("\nError opening the file %s\n",file); exit(0); } LinesPerEvent=0; TotalEnergyPerEvent= 0.0; E_Array[LinesPerEvent]=0.0; EnergyDepositedOuterLayer=0.0; // data collected per event for(iCount=1;iCount<TL+1;iCount++){ L[iCount]=0; EndCap1[iCount]=0.0; EndCap1[iCount]=0.0; Barrel[iCount]=0.0; } while(!feof(in)) { // Loop over all the rows and add the energy.. energy=0.0; fscanf(in,"%d %d %d %d %d %d %f %f %f %lf %d %d",&p,&s,&m,&ii,&jj,&k,&e,&e,&e,&energy,&t,&t);

86

if(energy==0)break; LinesPerEvent++; // to keep track of none zero energy deposited cells P1[LinesPerEvent]=p; S1[LinesPerEvent]=s; M1[LinesPerEvent]=m; I1[LinesPerEvent]=ii; J1[LinesPerEvent]=jj; K1[LinesPerEvent]=k; Checked_Array[LinesPerEvent]=0; E_Array[LinesPerEvent]=GainFactor*energy; // energy density calculation if(p>P_Max) P_Max=p; else if(p<P_Min) P_Min=p; if (k==40 && (p==Hcal_Barrel || p==Hcal_EndCap_plusZ || p==Hcal_EndCap_negZ)) { fprintf(out5,"%lf\n",E_Array[LinesPerEvent]); EnergyDepositedOuterLayer=EnergyDepositedOuterLayer+E_Array[LinesPerEvent]; OLED+=E_Array[LinesPerEvent]; if(Debug) printf("Outer Layer Line#: %d Current File: %d Energy: %lf Total:%lf\n",LinesPerEvent,CurrentFile,E_Array[LinesPerEvent],OLED); } TotalEnergyPerEvent= TotalEnergyPerEvent+E_Array[LinesPerEvent]; if(Debug==1)printf("CurrentFile %d Total Energy %lf\n",CurrentFile,TotalEnergyPerEvent); } // End while TotalEnergyAllEvents+=TotalEnergyPerEvent; fprintf(out4,"%lf\n",TotalEnergyPerEvent); fprintf(out6,"%lf %lf\n",TotalEnergyPerEvent,EnergyDepositedOuterLayer); { //beginning of cell energy studies cell_number=1; n_above=0; int nHits=1; Total_Energy=TotalEnergyPerEvent; // cell study loop begins for(i=1;i<LinesPerEvent;i++) {

87

if (Checked_Array[i]==0){ Total_Energy=E_Array[i]; Checked_Array[i]=cell_number; nHits=1; for(j=i+1;j<LinesPerEvent;++j) { if(P1[j]==P1[i] && S1[j]==S1[i] && M1[j]==M1[i] && I1[j]==I1[i] && J1[j]==J1[i] && K1[j]==K1[i] && Checked_Array[j]==0) { Checked_Array[j]=cell_number; nHits++; Total_Energy=Total_Energy+E_Array[j]; } } if(Debug==1) printf("Cell#:%d Energy:%10.5f %d\n",cell_number,Total_Energy,nHits); fprintf(out3,"%d\n",nHits); fprintf(out0,"%lf\n",Total_Energy); // Write to a file.. L[K1[i]]=L[K1[i]]+1; fprintf(out8,"%d\n",K1[i]); if(P1[i]==P_Max){ EndCap2[K1[i]]=EndCap2[K1[i]]+Total_Energy; printf("Energy Density -EndCap2 %lf\n",EndCap2[K1[i]]); } else if(P1[i]==P_Min) { EndCap1[K1[i]]=EndCap1[K1[i]]+Total_Energy; printf("Energy Density -EndCap1 %lf\n",EndCap1[K1[i]]); } else { Barrel[K1[i]]=Barrel[K1[i]]+Total_Energy; } if(Total_Energy>MaxEnergy)MaxEnergy=Total_Energy; if(Total_Energy>Threshold)n_above++; ++cell_number; } } //cell study loop ends // actual numeber of cells if(cell_number>1)

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cell_number=--cell_number; else { //if there is only one line in the file if(Total_Energy>Threshold)n_above++; fprintf(out3,"%d\n",nHits); fprintf(out0,"%lf\n",Total_Energy); fprintf(out8,"%d\n",K1[i]); } if(Debug==1 && n_above==0) printf("Current File %d Found %d cells above Threshold in %d lines\n",CurrentFile,n_above,LinesPerEvent); fprintf(out1,"%d\n",n_above); fclose(in); // output to number of cells hit distribution in layers and dE/dx Piece=0; fprintf(out9,"%d ",Piece); for(iCount=1;iCount<TL+1;iCount++) { fprintf(out7,"%d %s",L[iCount]," "); fprintf(out9,"%lf %s",EndCap1[iCount]," "); } fprintf(out7,"\n"); Piece=1; fprintf(out9,"\n%d ",Piece); for(iCount=1;iCount<TL+1;iCount++) { fprintf(out9,"%lf %s",Barrel[iCount]," "); printf("CurrentFile %d Energy Density -Barrel Layer # %d %lf \n",CurrentFile,iCount,Barrel[iCount]); } Piece=2; fprintf(out9,"\n%d ",Piece); for(iCount=1;iCount<TL+1;iCount++) { fprintf(out9,"%lf %s",EndCap1[iCount]," "); } fprintf(out9,"\n"); if(n_above==0){ printf("Current File %d Lines in the file: %d\n",CurrentFile,LinesPerEvent); } if(Debug==1) printf("Total Live Energy %10.5f Number of cells above threshold %d\n",TotalEnergyPerEvent,n_above);

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fprintf(out2,"%lf %d\n",TotalEnergyPerEvent,n_above); } //end of cell energy studies CurrentFile++; TotalEnergyPerEvent=0.0; if(Threshold>0)printf("Cells %d cells above threshold %d\n",cell_number,n_above); } //End outer most while result=fflush(out0); if(result>0) { printf("%d Error in flushing\n",result); exit(0); } fclose(out0); fclose(out1); fclose(out2); fclose(out3); fclose(out4); fclose(out5); fclose(out6); fclose(out7); fclose(out8); fclose(out9); printf("\nDone.. Energy Deposited in Outer Layer of Hcal %lf\n",OLED); printf("TotalEnergyAllEvents: %10.3f Total Number of Events: %d\n",TotalEnergyAllEvents,num_events); printf("GainFactor:%f Threshold:%f Number of arguments:%d P_Min %d P_Max %d\n",GainFactor,Threshold,ac,P_Min,P_Max); } // A function used to append strings to other strings.. char *strapp( char *src1, char *src2) { int len; char *dest; char *p; const char *q; len = strlen(src1); len += strlen(src2); dest = ( char *) malloc( len * sizeof(char) ); p = dest;

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q = src1; while (*q != '\0') { *p = *q; p++; q++; } q = src2; while (*q != '\0') { *p = *q; p++; q++; } *p ='\0'; return dest; } Description: GetTotalLiveEnergy.C //Latest and greatest April 05,2003 // Combine data from two input files into one output file #include <stdio.h> #include <stdlib.h> int main( int ac, char **av) { FILE *in1, *in2, *out; int debug=1,ch=0; double energyEM, energyHC,total,t = 0.0,GainFactor=1.0; double EM,EH,PredominanceFactor1=0,PredominanceFactor2=0.90; int iCounter=0,hist,MultipleHistograms=0,result; if( ac < 2) { printf("\nUsage:GetTotalLiveEnergy <file1> <file2> <OutputFile> <GainFactor> <Multiple> <PredominanceFactor1> <PredominanceFactor2>\n"); exit(0); } printf("%s %s\n",av[1],av[2]); if( (in1 = fopen(av[1],"r")) == NULL ) { printf("\nError opening the file %s\n",av[1]); exit(0); } if( (in2 = fopen(av[2],"r")) == NULL ) { printf("\nError opening the file %s\n",av[1]); exit(0);

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} if( (out = fopen(av[3],"w")) == NULL ) { printf("\nError opening the file %s\n",av[3]); exit(0); } if(ac>3) { if(atof(av[4])>0)GainFactor=atof(av[4]); } if(ac>4) { if(atoi(av[5])>0){ MultipleHistograms=1; if(ac>5 && atof(av[6])>0)PredominanceFactor1=atof(av[6]); if(ac>6 && atof(av[7])>0)PredominanceFactor2=atof(av[7]); } } while(!feof(in1) && !feof(in2)) { //reading input files loop fscanf(in1,"%lf",&energyEM); fscanf(in2,"%lf",&energyHC); energyHC=GainFactor*energyHC; if(debug)printf("%d EM: %10.3e HC: %10.3e\n",iCounter,energyEM,energyHC); if(feof(in1)) break; iCounter++; total = energyEM + energyHC; if(total==0){ printf("Zero......................................%d\n",iCounter); printf("%d EM: %10.3e HC: %10.3e\n",iCounter,energyEM,energyHC); ch=getchar(); } if(MultipleHistograms) { if (total>0){ EM=energyEM/total; EH=energyHC/total; if(EM>=PredominanceFactor1 && EM<=PredominanceFactor2) hist=0; else if(EH>=PredominanceFactor1 && EH<=PredominanceFactor2) hist=1; else hist=2; } //changed on May 23, 03

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else hist=2; fprintf(out,"%d %15.8lf %8.4f %8.4f\n", hist, total,EM,EH); } else //if(total>0) // changed on May 23, 03 fprintf(out,"%15.8lf\n", total); t += total; } // reading input files loop ends printf("Total Energy deposited %15.8lf in %d Events\n",t,iCounter); fclose(in1); fclose(in2); result=fflush(out); fclose(out); return 0; } Description:TotalLiveHist.C // latest and greatest 06/05/2003 { // read data from a file and plot distribution of data, fits the data and then set range of fit using σ3± if the fit is Gaussian. // Plot distribution of live energy gROOT->Reset(); #include <iostream.h> #define InputFile "50GeV.Total" #define RootFile "RootFiles/50GeV.root" #define PostScriptFile "PostScripts/50GeV.ps" #define DisplayText "" #define X_Axis_Title "(Energy Deposited)/Event (MeV)" #define Y_Axis_Title "# of Events" #define startRange 350 #define endRange 2000 #define SetRange 0 #define Correction 1 #define DisplayStatistics 0 #define CreateRootFile 1 #define CreatePostScriptFile 1 #define Fit "gaus" #define nBins 100 ifstream in; Option_t *opt; in.open(InputFile, ios::in);

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Float_t x,xMaximum=0; Int_t nlines = 0; // properties of histograms if(DisplayStatistics==0) gStyle->SetOptStat(0); else gStyle->SetOptStat(1110); gStyle->SetOptFit(); gStyle->SetPalette(1); gStyle->SetCanvasColor(33); gStyle->SetFrameFillColor(18); TCanvas *c1=new TCanvas("c1","Energy Histogram",10,10,1200,850); if(Fit=="gaus")c1->Divide(1,2); if(CreateRootFile>0) TFile *f = new TFile(RootFile,"RECREATE"); TH1F *h1 = new TH1F("h1",DisplayText ,nBins,startRange,endRange); c1->cd(1); gPad->GetFrame()->SetFillColor(18); gPad.Draw(); while (1) { in >> x; x=x/Correction; if (!in.good()) break; if(x>xMaximum)xMaximum=x; h1->Fill(x); printf("%10.5f\n",x); nlines++; } h1->Draw("EP"); h1->SetLineColor(2); h1->GetXaxis()->SetTitle(X_Axis_Title); h1->GetXaxis()->CenterTitle(); h1->GetYaxis()->SetTitle(Y_Axis_Title); h1->GetYaxis()->CenterTitle(); h1->Draw("EP"); Int_t i=int (xMaximum); printf("Maximum %d\n",i); if(SetRange)h1->GetXaxis()->Set(nBins,startRange,xMaximum);

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h1->GetYaxis()->CenterTitle(); h1.Fit(Fit); h1.Draw("e1P"); TF1 *myFunc=h1->GetFunction(Fit); Double_t Mean=myFunc->GetParameter(1); Int_t nPoints=myFunc->GetNumberFitPoints(); Double_t xMin=myFunc->GetXmin(); Double_t xMax=myFunc->GetXmax(); Int_t nPx=myFunc->GetNpx(); printf("xMin %10.5f xMax %10.5f nPx %d Number of fitted points %d\n",xMin,xMax,nPx,nPoints); Double_t sigma=myFunc->GetParameter(2); if(Fit=="gaus"){ Double_t startRangeFit=Mean-3*sigma; Double_t endRangeFit=Mean+3*sigma; TH1F *h1_F=(TH1F*)h1->Clone(); h1_F->SetName("h1_F"); c1->cd(2); h1_F->SetLineColor(kBlue); h1_F->Draw("E1P"); h1_F.Fit(Fit,"R",opt,startRangeFit,endRangeFit); h1_F->Draw("e1P"); } c1->cd(); if(CreatePostScriptFile) c1->Print(PostScriptFile); printf(" File has %d Lines sigma: %10.5f Number of points fitted:%d\n",nlines,sigma,nPoints); printf(" Max %10.5f\n",xMaximum); in.close(); if(CreateRootFile>0) f->Write(); } Description: Multiple.C - Plot Multiple plots (EM and HC, for Weighting Factor calculation) { // example of macro to read data from an ascii file and // create a root file with an histogram and an ntuple. gROOT->Reset(); #include <iostream.h> #define InputFile "50GeV.total" #define RootFile "RootFiles/50GeV_M.root" #define DisplayText "" #define PostScriptFile "PostScripts/50GeV_M.ps" #define CreatePostScriptFile 1 #define CreateRootFile 1

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#define startRange 0 #define endRange 8500 #define startEMRange 200 #define endEMRange 1800 #define Correction 1 #define DisplayStatistics 0 #define X_Axis_Title "(Energy Deposited)/Event (MeV)" #define Y_Axis_Title "# of Events" #define EC_Fit "gaus" #define HC_Fit "gaus" #define Fit "landau" #define nBinsEM 30 ifstream in; Option_t *opt; in.open(InputFile, ios::in); Float_t x,xMax=0,y,z; Int_t nlines = 0,nBins=100,n,ch; // properties of histograms if(DisplayStatistics) gStyle->SetOptStat(1111); else gStyle->SetOptStat(0); gStyle->SetOptFit(); gStyle->SetPalette(1); gStyle->SetCanvasColor(33); gStyle->SetFrameFillColor(18); TCanvas *c1=new TCanvas("c1","Energy Histogram",10,10,1200,850); c1->Divide(2,2); if(CreateRootFile) TFile *f = new TFile(RootFile,"RECREATE"); TH1F *h_EM = new TH1F("h_EM",DisplayText,nBinsEM,startEMRange,endEMRange); TH1F *h_HC = new TH1F("h_HC","",nBins,startRange,endRange); TH1F *h_R = new TH1F("h_HR","",nBins,startRange,endRange); TH1F *h_T = new TH1F("h_T","",nBins,startRange,endRange); c1->cd(1); gPad->GetFrame()->SetFillColor(18); gPad.Draw(); while (1) { in >> n>>x>>y>>z;

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x=x/Correction; printf("Line: %d %d %10.3e %10.3e %10.3e\n",nlines,n,x,y,z); if (!in.good()) break; if(x>xMax)xMax=x; h_T->Fill(x); if(n==0) { h_EM->Fill(x); } else if (n==1) h_HC->Fill(x); else h_R->Fill(x); nlines++; } h_EM->Draw("HIST"); h_EM->SetLineColor(2); h_EM->GetXaxis()->SetTitle(X_Axis_Title); h_EM->GetXaxis()->CenterTitle(); h_EM->GetYaxis()->SetTitle(Y_Axis_Title); h_EM->GetYaxis()->CenterTitle(); h_EM->Draw("HIST"); h_EM.Fit(EC_Fit); h_EM->Draw("E1P"); TF1 *myFunc=h_EM->GetFunction(EC_Fit); Double_t Mean=myFunc->GetParameter(1); Double_t sigma=myFunc->GetParameter(2); Double_t startRangeFit=Mean-3*sigma; Double_t endRangeFit=Mean+3*sigma; if(EC_Fit=="gaus")h_EM.Fit(EC_Fit,"R",opt,startRangeFit,endRangeFit); Int_t n1=myFunc->GetNumberFitPoints(); Int_t n2=myFunc->GetNpx(); h_EM->Draw("E1P"); printf(" number of fit points %d number of points used %d\n",n1,n2); c1->cd(2); h_HC->SetLineColor(kBlue); h_HC->Draw("HIST"); h_HC->GetXaxis()->SetTitle(X_Axis_Title); h_HC->GetXaxis()->CenterTitle(); h_HC->GetYaxis()->SetTitle(Y_Axis_Title); h_HC->GetYaxis()->CenterTitle();

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h_HC->Draw("HIST"); h_HC.Fit(HC_Fit); h_HC->Draw("E1P"); TF1 *myFunc=h_HC->GetFunction(HC_Fit); Double_t Mean=myFunc->GetParameter(1); Double_t sigma=myFunc->GetParameter(2); Double_t startRangeFit=Mean-3*sigma; Double_t endRangeFit=Mean+3*sigma; if(HC_Fit=="gaus") h_HC.Fit(HC_Fit,"R",opt,startRangeFit,endRangeFit); h_HC->Draw("E1P"); Int_t n1=myFunc->GetNumberFitPoints(); Int_t n2=myFunc->GetNpx(); printf(" number of fit points %d number of points used %d\n",n1,n2); c1->cd(3); h_R->SetLineColor(kBlue); h_R->Draw("HIST"); h_R->GetXaxis()->SetTitle(X_Axis_Title); h_R->GetXaxis()->CenterTitle(); h_R->GetYaxis()->SetTitle(Y_Axis_Title); h_R->GetYaxis()->CenterTitle(); h_R->Draw("HIST"); h_R.Fit(Fit); h_R->Draw("E1P"); c1->cd(4); h_T->SetLineColor(kRed); h_T->Draw("HIST"); h_T->Fit(Fit); h_T->GetXaxis()->SetTitle(X_Axis_Title); h_T->GetXaxis()->CenterTitle(); h_T->GetYaxis()->SetTitle(Y_Axis_Title); h_T->GetYaxis()->CenterTitle(); h_T->Draw("E1P"); if(CreatePostScriptFile) c1->Print(PostScriptFile); printf(" found %d points\n",nlines); printf(" Max %10.5f\n",xMax); c1->cd(); in.close(); if(CreateRootFile)f->Write(); }

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Description: Response.C – to plot response curve and fit the curve using linear fit. { #define DisplayTitle 0 #define DisplayCorrectedErr 0 Int_t n=11; TCanvas *c=new TCanvas("c","Mokka GEM Digital Response Curve",-4,27,1212,771); gStyle->SetOptFit(); gStyle->SetOptStat(0); Double_t E[n]={1,1.75,2.5,3,4,5,10,20,50,75,100}; Double_t E_Mean[n]={24.23,41.41,57.8,70.71,100.7,125,273,559,1378,1984,2552}; Double_t errE_Mean[n]={0.1186,0.2181,0.2943,0.3245,0.329,0.4832,1.272,1.823,3.063,3.936,4.768}; Double_t errE[n]={0,0,0,0,0,0,0,0,0,0,0}; Double_t errFitted[n]; for(Int_t i=0;i<n;i++) { E_Mean[i]=E_Mean[i]*0.001; errE_Mean[i]=errE_Mean[i]*0.001; errFitted[i]=errE_Mean[i]*sqrt(108.5/4); } TGraph *gr=new TGraphErrors(n,E,E_Mean,errE,errE_Mean); gr->Draw("AC"); gr->Fit("pol1"); TF1 *myFunc=gr->GetFunction("pol1"); myFunc->SetParameter(0,0); Double_t slopeE_Mean=myFunc->GetParameter(1); gr->SetLineColor(45); gr->GetXaxis()->SetLabelSize(0.02); gr->GetYaxis()->SetLabelSize(0.02); gr->GetYaxis()->SetTitle("<E_{live}> (GeV)"); gr->GetXaxis()->SetTitle("E_{#pi} (GeV)"); TPaveStats *st=(TPaveStats*) gPad->GetPrimitive("stats"); st->SetX1NDC(0.126884); st->SetX2NDC(0.7546); Char_t str[100]; if(DisplayTitle){

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sprintf(str, "Mokka TDR Response Curve - Slope %8.5f ",slopeE_Mean); gr->SetTitle(str); } else { sprintf(str,"<E_{Live}>=%5.2f E_{#pi}",slopeE_Mean); gr->SetTitle(str); } if(DisplayCorrectedErr) { Double_t chi=myFunc->GetChisquare(); Int_t dof=myFunc->GetNDF(); for(Int_t i=0;i<n;i++) { errFitted[i]=errE_Mean[i]*sqrt(chi/dof); } TGraph *gr1=new TGraphErrors(n,E,E_Mean,errE,errFitted); gr1->SetLineColor(2); gr1->SetLineWidth(3); gr1->Draw("CP"); gr1->Fit("pol1"); gr1->SetTitle(""); TF1 *myFunc=gr1->GetFunction("pol1"); myFunc->SetParameter(0,0); Double_t slopeE_Mean=myFunc->GetParameter(1); c->Modified(); } c->cd(); c->Print("PostScripts/Response.ps"); } Description: Resolution.C – to plot Resolution curve and fit the curve { #define WithErrors 1 #define DisplayText "Mokka GEM" TCanvas *c=new TCanvas("c","Mokka GEM Digital Resolution"); c->Divide(1,2); gStyle->SetOptFit(); TFile *f=new TFile("RootFiles/Resolution.root","RECREATE"); Int_t n=11; Double_t y[n],ey[n];

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Double_t Mean[n]={0.9187,1.62,2.229,2.789,3.822,4.752,10.41,21.21,52.16,75.24,97.07}; Double_t x[n]; Double_t Sigma[n]={0.3486,0.641,0.8541,0.9674,1.154,1.523,2.943,4.545,7.253,9.057,11.22}; Double_t deltaMean[n]={0.0045,0.008,0.0115,0.01239,0.01254,0.01816,0.051,0.0633,0.1173,0.1471,0.1818}; Double_t deltaSigma[n]={0.0035,0.006364,0.0089,0.009275,0.008763,0.0144,0.03438,0.045,0.0882,0.1163,0.1718}; Double_t ex[n]; Int_t j; for(Int_t i=0;i<n;i++){ j=n-1-i; y[i]=(Sigma[i]/Mean[i])*100; ey[i]=(Sigma[i]/Mean[i])*(deltaMean[i]/Mean[i]+deltaSigma[i]/Sigma[i]); ex[i]=0.5*deltaMean[i]/Mean[i]; x[i]=1.0/sqrt(Mean[i]); ex[i]=x[i]*ex[i]; printf("j=%d %lf\n ",j,y[j]); } if(WithErrors) { TGraph *gr=new TGraphErrors(n,x,y,ex,ey); TGraph *gr2=new TGraphErrors(n,Mean,y,deltaMean,ey); } else { TGraph *gr=new TGraph(n,x,y); TGraph *gr2=new TGraph(n,Mean,y); } c->cd(1); gr->Fit("pol1","E"); gr->GetFunction("pol1")->SetLineColor(kBlue); Double_t intercept=gr->GetFunction("pol1")->GetParameter(0); Double_t slope=gr->GetFunction("pol1")->GetParameter(1); Double_t chi=gr->GetFunction("pol1")->GetChisquare();

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Int_t dof=gr->GetFunction("pol1")->GetNDF(); Char_t str[150]; sprintf(str,"Mokka GEM - Digital Analysis- Resolution %10.5f %s Intercept %10.5f %s",slope,"%",intercept,"%"); gr->Draw("A*"); gr->GetYaxis()->SetLabelSize(0.03); gr->GetXaxis()->SetLabelSize(0.03); gr->GetXaxis()->SetTitle("1/#sqrt{<E>} (MeV)"); gr->GetYaxis()->SetTitle("#sigma/<E> (%)"); gr->SetTitle(""); TPaveStats *st=(TPaveStats*)gPad->GetPrimitive("stats"); st->SetX1NDC(0.11679); st->SetX2NDC(0.475911); c->Modified(); c->cd(2); gStyle->SetOptFit(0); gr2->SetLineColor(2); gr2->Draw("A*"); gr2->GetXaxis()->SetTitle("<E> (MeV)"); gr2->GetYaxis()->SetTitle("#sigma/<E> (%)"); gr2->GetXaxis()->SetLabelSize(0.03); gr2->GetYaxis()->SetLabelSize(0.03); gr2->SetTitle(""); TF1 *f1=new TF1("f1","[1]*sqrt(1/x)+[0]"); f1->SetLineColor(kBlue); f1->SetParameter(0,intercept); f1->SetParameter(1,slope); gr2->Fit(f1); leg=new TLegend(0.4,0.6,.89,0.89); sprintf(str,"#sigma/<E>=#frac{%5.2f%s}{#sqrt{<E>}}+%5.2f%s #frac{#chi^{2}}{dof}=#frac{%5.2f}{%d}",slope,"%",intercept,"%",chi,dof); leg->AddEntry(f1,str,"L"); leg->Draw(); c->Modified(); c->cd(); f->Write(); c->Print("PostScripts/Resolution.ps"); }

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Description: DS.C - Digital Study plot dE/dN // Latest Code for Digital Analysis 05/12/2003 { #include <stdlib.h> #include <errno.h> #include <sys/types.h> #include <sys/stat.h> #include <fcntl.h> #include <iostream.h> extern int errno; gROOT->Reset(); TStyle *plain=new TStyle("Plain","Plain Style"); Color_t color=kRed; Style_t style=27; Size_t size=0.6; plain->SetMarkerColor(color); plain->SetMarkerSize(size); plain->SetMarkerStyle(style); plain->cd(); gStyle->SetOptStat(kFALSE); gStyle->SetOptFit(); gStyle->SetPalette(1); gStyle->SetCanvasColor(33); gStyle->SetFrameFillColor(18); // define variables #define InputFile "AllE.dat" #define RootFile "RootFiles/AllE.root" #define PostScriptFile "PostScripts/AllE.ps" #define startYRange 0 #define endXRange 1050 #define startXRange 0 #define endYRange 25334 #define startFitRegion 0 #define endFitRegion 1050 #define SetFitParameters 0 #define Slope 12.5 // Start Range and Final Range for Histogram. You can change.. #define nXBins 100 #define nYBins 100 // Number of Bins - you can change

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#define LogScale 0 #define CreateRootFile 1 #define CreatePostScript 1 #define xleg 0.117148 #define yleg 0.875392 // Text to display on Histogram #define DisplayText "Mokka GEM - GainFactor 3500" #define CanvasText "Mokka GEM" #define X_Axis_Title "# of Cells/Event" #define Y_Axis_Title "Energy Deposited in Hcal/Event (MeV)" #define Correction 1 Int_t nMax=0,Debug=1,n=0; Double_t E, MaxEnergy=0.0,n_above=0; Int_t nlines = 0,i,num_events=1; // root file if(CreateRootFile>0) TFile *f = new TFile(RootFile,"RECREATE"); TCanvas *c1 = new TCanvas("c1", "Digital Study",0,0,1013,740); c1->Divide(1,2); c1->cd(1); c1->Range(0,0,1,1); c1->SetFillColor(40); c1->SetBorderSize(2); c1->SetLeftMargin(0.75); c1->SetBottomMargin(0.25); // ------------>Primitives in pad: c1_2 TPad *c1_2 = new TPad("c1_2", "c1_2",0.0170648,0.145408,0.996587,0.994898); c1_2->Draw(); c1_2->cd(); c1_2->Range(-4769.13,-2.00602e+06,42922.1,7.53233e+06); c1_2->SetFillColor(33); c1_2->SetBorderSize(2); c1_2->SetBorderMode(0); c1_2->SetFrameFillColor(18); if(LogScale)c1_2->SetLogy(); TH2F *h2d=new TH2F("h2d",DisplayText,nXBins,startXRange,endXRange,nYBins,startYRange,endYRange);

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TProfile *h2=new TProfile("h2",DisplayText,nXBins,startXRange,endXRange,startYRange,endYRange,"G"); // Open Input file ifstream in; in.open(InputFile,ios::in); while (1) { in >> E>>n; E=E/Correction; if (!in.good()) break; if(Debug)printf("%10.5f %d\n",E,n); n_above=n; h2d->Fill(n_above,E); h2->Fill(n_above,E,1); if(n>nMax)nMax=n; if(E>MaxEnergy)MaxEnergy=E; nlines++; } in.close(); if(Debug) printf(" Number of lines in the Input file %d\n",nlines); Style_t font=62; c1->cd(1); h2->Draw(""); Int_t i=int (MaxEnergy); printf("Maximum %d\n",i); h2->GetXaxis()->SetTitle(X_Axis_Title); h2->GetXaxis()->CenterTitle(); h2->GetYaxis()->SetLabelSize(0.03); h2->GetXaxis()->SetLabelSize(0.03); h2->GetYaxis()->SetTitle(Y_Axis_Title); h2->GetYaxis()->CenterTitle(); h2->Draw(""); Option_t *opt; h2.Fit("pol1","R",opt,startFitRegion,endFitRegion); TF1 *func=h2->GetFunction("pol1"); if(SetFitParameters){ func->SetParameter(0,0); func->SetParameter(1,Slope); } Double_t yIntercept=func->GetParameter(0); Double_t slope=func->GetParameter(1); Double_t slope_Err=func->GetParError(1);

105

Double_t yIntercept_Err=func->GetParError(0); Char_t str[100]; printf("Y intercept %10.3e Err %10.3e Slope %10.3e Err %10.3e\n",yIntercept,yIntercept_Err,slope,slope_Err); sprintf(str, "Y intercept %10.3e Err %10.3e Slope %10.3e Err %10.3e",yIntercept,yIntercept_Err,slope,slope_Err); // h2->FitSlicesY(0,10,30); printf("Max Hcal Energy %10.5f Maximum number of cells %d\n",MaxEnergy,nMax); TLegend *leg = new TLegend(0.31038,0.251287,0.887836,0.151802,NULL,"brNDC"); leg->SetLineColor(1); leg->SetFillStyle(1001); leg->SetLineWidth(1); leg->SetTextSize(0.04); TLegendEntry *entry=leg->AddEntry(h2,str); gStyle->SetOptStat(); leg->Draw(); c1->cd(2); h2d->Draw(); h2d->GetYaxis()->SetLabelSize(0.03); h2d->GetXaxis()->SetLabelSize(0.03); h2d->GetXaxis()->SetTitle(X_Axis_Title); h2d->GetXaxis()->CenterTitle(); h2d->GetYaxis()->SetLabelSize(0.03); h2d->GetXaxis()->SetLabelSize(0.03); h2d->GetYaxis()->SetTitle(Y_Axis_Title); h2d->GetYaxis()->CenterTitle(); if(CreateRootFile>0)f->Write(); if(CreatePostScript>0) c1->Print(PostScriptFile); } Description: HitsFrequency.C – to plot fractional number of hits/cell distribution // Latest and greatest 05/26/2003 { #include <iostream.h> gROOT->Reset(); #define startRange -0.5 // Start Range and Final Range for Histogram. You can change.. #define endRange 5.5

106

#define nBins 6 // Number of Bins - you can change #define InputFile "../3GeV/Hcal/CO.dat" #define RootFile "RootFiles/3CO.root" #define strPaveText "3 GeV Pions - 9977 Events " #define PostScriptFile "PostScripts/3CO.ps" #define DisplayText "Mokka GEM"// Display Message on the Canvas #define debug 0 #define YaxisTitle "fractional hits" #define XaxisTitle "# of hits on a cell" #define DisplayTextOnHist "" #define CreateRootFile 1 #define CreatePostScript 1 // Text to display on Histogram Double_t E; Float_t TotalPercentage=0; Int_t nlines = 0,i,N,MaxN=0; // Open Input file ifstream in; // Input file - You can change in.open(InputFile,ios::in); // root file if(CreateRootFile)TFile *f = new TFile(RootFile,"RECREATE"); gStyle->SetOptStat(0); gStyle->SetPalette(1); gStyle->SetCanvasColor(33); gStyle->SetFrameFillColor(18); TCanvas *c1=new TCanvas("c1",DisplayText,8,8,1000,1000); c1->Range(0,0,1,1); c1->SetFillColor(40); c1->SetBorderSize(2); // ------------>Primitives in pad: c1_2 TPad *c1_2 = new TPad("c1_2", "c1_2",0.0170648,0.145408,0.996587,0.994898); c1_2->Draw(); c1_2->cd(); c1_2->Range(-3.125,-556.106,28.125,5004.96); c1_2->SetFillColor(33);

107

c1_2->SetBorderSize(2); c1_2->SetFrameFillColor(18); TH1F *hf = new TH1F("hf","",nBins,startRange,endRange); Double_t total=0.0; while (1) { in >> E; N=E; if (!in.good()) break; if(N>0){ if(debug)printf("%d\n",N); hf->Fill(N); total=total+E; if(N>MaxN)MaxN=N; } // only for nHits>=0 nlines++; } in.close(); total=hf->GetEntries(); printf("Total Entries %d\n",total); TH1F *h1 = new TH1F("h1",DisplayTextOnHist,nBins,startRange,MaxN); for(Int_t i=1;i<nBins+1;i++) { N=hf->GetBinContent(i); TotalPercentage+=N/total; printf("Hits # %d Content %lf\n",i-1,N); h1->Fill(i-1,N/total); } printf("# of lines in the file %d Total %d Percentage %lf\n",nlines,total,TotalPercentage); h1->Draw("HIST"); h1->SetLineColor(13); h1->GetXaxis()->SetTitle(XaxisTitle); h1->GetXaxis()->CenterTitle(); h1->GetXaxis()->SetLabelSize(0.03); h1->GetYaxis()->SetLabelSize(0.03); h1->GetYaxis()->SetTitle(YaxisTitle); Float_t xMax=MaxN+0.5; Int_t nBinsU= (MaxN+1); h1->GetYaxis()->CenterTitle();

108

h1->SetFillColor(45); h1->Draw("HIST"); h1->SetLineColor(kBlue); c1->cd(); pt = new TPaveText(0.0290102,0.0255102,0.989761,0.112245,"br"); pt->SetFillColor(18); TText *text = pt->AddText(strPaveText); pt->Draw(); c1->Modified(); c1->cd(); printf(" Range %10.1f New Bins %d\n",xMax,nBinsU); if(CreatePostScript>0) c1->Print(PostScriptFile); if(CreateRootFile>0) f->Write(); } Description: Number of ion-electron pairs produced using w=mean ionization energy required to produce an ion-electron pair. // Latest and greatest 06/02/03 { #include <iostream.h> gROOT->Reset(); #define startRange 0 // Start Range and Final Range for Histogram. You can change.. #define endRange 0.008 #define endIonPairsRange 140 #define nBins 100 // Number of Bins - you can change #define InputFile "100GeV.hcal" #define DisplayTextOnHist "" // Text to display on Histogram #define RootFile "RootFiles/100GeV_IP_Hcal.root" #define PostScriptFile "PostScripts/100GeV_IP_Hcal.ps" #define DisplayText "Mokka GEM"// Display Message on the Canvas #define W 26.4 //eV units #define Debug 1 #define LogScale 1 #define Fit "landau" #define DoFit 0 #define Response 1 #define GeV_Conversion 0 char str[100]; Float_t E,MaxEnergy=0.0;

109

Color_t Color=kRed; Int_t nlines = 0,i,nIonsPairs,nMax=0; // Open Input file ifstream in; // Input file - You can change in.open(InputFile,ios::in); // root file TFile *f = new TFile(RootFile,"RECREATE"); gStyle->SetOptStat(0); gStyle->SetPalette(1); gStyle->SetCanvasColor(33); gStyle->SetFrameFillColor(18); gStyle->SetOptFit(0111); TCanvas *c1=new TCanvas("c1",DisplayText,8,8,900,900); c1->Range(0,0,1,1); c1->SetFillColor(40); c1->SetBorderSize(2); // ------------>Primitives in pad: c1_2 TPad *c1_2 = new TPad("c1_2", "c1_2",0.0170648,0.145408,0.996587,0.994898); c1_2->Divide(1,2); c1_2->Draw(); c1_2->Range(-3.125,-556.106,28.125,5004.96); c1_2->SetFillColor(33); c1_2->SetBorderSize(2); c1_2->SetFrameFillColor(18); if(LogScale==1) c1_2->SetLogy(); c1_2->cd(1); if(strlen(DisplayTextOnHist)>0)sprintf(str,"Energy Distribution for %s",DisplayTextOnHist); TH1F *h1 = new TH1F("h1",str,nBins,startRange,endRange); if(strlen(DisplayTextOnHist)>0)sprintf(str,"Number of Ion-Pair Distribution for %s",DisplayTextOnHist); TH1F *h_nIonsPair = new TH1F("h_IonsPairs",str,nBins,startRange,endIonPairsRange); while (1) { in >> E; E=E/Response;

110

nIonsPairs=E*(1.0E06)/W; if(GeV_Conversion) E=E/1000.0; if (!in.good()) break; if(nIonsPairs>nMax)nMax=nIonsPairs; h_IonsPairs->Fill(nIonsPairs); h1->Fill(E); if(E>MaxEnergy)MaxEnergy=E; nlines++; } in.close(); printf(" Number of lines in the Input file %d\n",nlines); h1->SetLineColor(Color); h1->Draw("HIST"); if (GeV_Conversion) h1->GetXaxis()->SetTitle("Energy deposited in Cell/Event (GeV)"); else h1->GetXaxis()->SetTitle("Energy deposited in Cell/Event (MeV)"); h1->GetXaxis()->CenterTitle(); if(DoFit) h1->Fit(Fit); h1->Draw(""); c1_2->cd(2); h_IonsPairs->SetLineColor(45); h_IonsPairs->SetFillColor(50); h_IonsPairs->GetXaxis()->SetTitle("Number of Ion-Pairs in Cell/Event"); h_IonsPairs->GetXaxis()->CenterTitle(); if(DoFit) h_IonsPairs->Fit(Fit); h_IonsPairs->Draw(""); c1_2->cd(); printf("Max Energy %lf Maximum Number of Ion-Pairs created in a cell/Event %d\n",MaxEnergy,nMax); c1->Print(PostScriptFile); f->Write(); } Description: To caculate the weighting factor { Int_t n=11; TCanvas *c=new TCanvas("c","Weighting Factor GEM Digital Study Gain 3500"); gStyle->SetOptFit();

111

gStyle->SetOptStat(); c->Divide(1,2); c->cd(1); Double_t E[n]={1,1.75,2.5,3,4,5,10,20,50,75,100}; Double_t EC[n]={23.93,38.96,55.46,75.88,101.2,121.8,238.9,526.6,1467,2037,2800}; Double_t HC[n]={93.02,162.4,260.7,313.4,402.5,539.9,1104,2129,4935,7013,8924}; Double_t errEC[n]={0.1341,0.303,0.54,0.5067,0.5346,0.707,3.275,9.422,77.92,148.2,155.1}; Double_t errHC[n]={27.24,1.917,2.241,2.911,2.069,2.817,6.226,9.667,18.04,21.76,27.77}; Double_t errE[n]={0,0,0,0,0,0,0,0,0,0,0}; for(Int_t i=0;i<n;i++) { EC[i]=EC[i]*0.001; HC[i]=HC[i]*0.001; errHC[i]=errHC[i]*0.001; errEC[i]=errEC[i]*0.001; } TGraph *gr1=new TGraphErrors(n,E,EC,errE,errEC); TGraph *gr2=new TGraphErrors(n,E,HC,errE,errHC); gr1->SetTitle("Weighting Factor GEM Digital Study Gain 3500"); gr1->Draw("ALP"); gr1->Fit("pol1"); gr1->SetLineColor(kBlue); gr2->SetLineColor(kBlue); TF1 *myFunc=gr1->GetFunction("pol1"); myFunc->SetParameter(0,0); Double_t slopeEC=myFunc->GetParameter(1); Double_t errSlopeEC=myFunc->GetParError(1); gr1->GetXaxis()->SetTitle("E_{#pi} (GeV)"); gr1->GetXaxis()->CenterTitle(); gr1->GetYaxis()->SetTitle("<E_{Ecal}> (GeV)"); gr1->GetYaxis()->CenterTitle(); leg=new TLegend(0.4,0.6,.89,0.89); leg->AddEntry(myFunc,"<E>=0.02484E_{#pi} #frac{#chi^{2}}{dof}=#frac{304.8}{9}","L"); leg->Draw(); c->cd(2); gr2->Draw("ALP");

112

gr2->Fit("pol1"); TF1 *myFunc=gr2->GetFunction("pol1"); myFunc->SetParameter(0,0); Double_t slopeHC=myFunc->GetParameter(1); Double_t errSlopeHC=myFunc->GetParError(1); Double_t W=slopeEC/slopeHC; Double_t errW=W*(errSlopeEC/slopeEC+errSlopeHC/slopeHC); Char_t str[100]; sprintf(str, "Weighting Factor %lf error %lf",W,errW); gr2->GetXaxis()->SetTitle("E_{#pi} (GeV)"); gr2->GetXaxis()->CenterTitle(); gr2->GetYaxis()->SetTitle("<E_{Hcal}> (GeV)"); gr2->GetYaxis()->CenterTitle(); gr2->SetTitle(str); leg=new TLegend(0.4,0.6,.89,0.89); leg->AddEntry(myFunc,"<E>=0.09517E_{#pi} #frac{#chi^{2}}{dof}=#frac{1894}{9}","L"); leg->Draw(); c->cd(); c->Print("PostScripts/Weight.gif"); }

113

APPENDIX C

GEM MANUFACTURING TECHNOLOGY

114

The GEM manufacturing technology has been developed at CERN in the

printed circuits workshop (EST-MT). A metal-clad polymer foil (copper on

kapton) is coated on both sides with a photosensitive layer and exposed to UV

light through a mask reproducing the desired holes' pattern. The metal is

chemically removed in the holes, and the foil is immersed in a solvent for

Kapton. The resulting foil has conductor on both sides, pierced by a high

density of holes (typically 70 µm in diameter at 140 µm pitch). Close to a

thousand GEMs of various shapes and sizes have been built so far, both for the

requirements of HEP experiments and for other applications

[http://dbnetra01.cern.ch:9000/pls/ttdatabase/display.item?itemtable=technology&it

em_id=165].

115

APPENDIX D

REMAINING PLOTS

116

Figure D.1: Weighting factor for Mokka TDR. HCALECAL EEW /=

From Fig D.2, it is observed that the linear fit poorly represents the data

[χ2/dof 6194/95] and that the fit improves as the power of a polynomial equation

increases. For our analysis a cubic fit was used.

117

Figure D.2: Response curve for Mokka GEM with threshold applied. The black curve in the top shows a cubic fit while in the bottom plot a quartet fit is shown

in black. Blue line shows a linear fit in both plots.

118

Figure D.3: Weighting factor for Mokka GEM with threshold applied.

Figure D.4: Energy distribution of 50 GeV pions using range (0,Xmax) where Xmax is the maximum datum in the data set.

119

Figure D.5: Energy distribution of 50 GeV pions using range for the best dof/2χ fit.

Figure D.6: Response curve of Mokka GEM - digital study with threshold applied. A nonlinear approach

120

Figure D.7: Distribution of converted energy for 50 GeV pions – the top plot employs (0,Xmax) range and the bottom plot employs the best dof/2χ range.

121

Figure D.8: Resolution of Mokka GEM – digital study with threshold applied. A

nonlinear approach

122

APPENDIX E

FITS USED IN THE ANALYSIS

123

Guas: A guassian function with 3 parameters:

)/)((*5.0exp(*)( 2210 ppxpxf −−=

Linear: A polynomial of degree one xppxf *)( 10 += Quadratic: A polynomial of degree two 2

210 **)( xpxppxf ++= Cubic: A polynomial of degree three 3

32

210 ***)( xpxpxppxf +++= Landau [http://wwwasdoc.web.cern.ch/wwwasdoc/shortwrupsdir/g110/top.html]:

124

APPENDIX E

TESLA

125

TESLA, a new large-scale facility, is currently being planned and

developed by an international collaboration at the Deutsches Elektronen-

Synchroton (DESY) in Hamburg, Germany [http://tesla.desy.de].

TESLA comprises two facilities: a 33-kilometer-long linear

accelerator developed in an international collaboration, which will

bring electrons into collision with their antiparticles, the positrons,

and a 4-kilometer-long electron accelerator driving a new kind of X-

ray lasers. Main features:

Ø Total length 33 km

Ø Two linear accelerators – 15 km each

Ø Accelerator tunnel – 5m diameter

Ø Collision energy of 500 GeV

Ø Operating temperature – 3K

126

APPENDIX G

TABLES

127

Table G.1 MOKKA TDR - RESPONSE DATA

Eπ (GeV) Mean Energy (MeV) Mean Energy (MeV) 5 140.8± 1.034 155± 0.9647 10 299± 2.291 324± 1.635 20 648.5± 5.897 687.1± 2.731 50 1859± 8.671 1831± 5.761 75 2750± 11.09 2698± 7.997 100 3669± 20.09 3634± 9.543

Table G.2a MOKKA TDR - RESOLUTION DATA Eπ (GeV) Mean Energy

(MeV) Sigma

5.0 4.136± 0.01762 1.257± 0.01271 10.0 8.712± 0.02666 2.38± 0.01476 20.0 18.33± 0.05728 4.771± 0.03189 50.0 49.03± 0.1147 10.59± 0.08067 75.0 72.15± 0.2133 15.39± 0.1411 100.0 96.48± 0.2524 19.76± 0.1689

Table G.2b MOKKA TDR - RESOLUTION DATA Eπ (GeV) Mean Energy

(MeV) Sigma

5.0 4.136± 0.01752 1.186± 0.01144 10.0 8.704± 0.02725 2.374± 0.01512 20.0 18.34± 0.05181 4.76± 0.03231 50.0 49.04± 0.1153 10.57± 0.08174 75.0 72.22± 0.2131 15.3± 0.1386 100.0 96.58± 0.2519 19.65± 0.1658

TABLE G.3 MOKKA GEM - WEIGHTING FACTOR Eπ (GeV) Mean Energy in EM

(MeV) Mean Energy in HC

(MeV) 5.0 114± 0.6571 354.7± 3.845 10.0 221.5± 2.399 804.3± 7.924 20.0 496.6± 13.78 1708± 13.9 50.0 1244± 200.4 4502± 29.08 75.0 2007± 87.43 6952± 40.53 100.0 2663± 127.6 9200± 50.35

128

TABLE G.4 MOKKA GEM – RESPONSE DATA Eπ (GeV) Mean Energy (MeV) Mean Energy (MeV)

5.0 105.7± 0.5041 96.71± 0.6779 10.0 215.6± 1.53 194± 1.738 20.0 469.6± 2.991 417.7± 4.577 50.0 1291± 6.504 1259± 5.693 75.0 2016± 10.02 1942± 8.982 100.0 2693± 11.94 2618± 11.64

TABLE G.5a MOKKA GEM - RESOLUTION DATA Eπ (GeV) Mean Energy (MeV) Sigma

5.0 4.041± 0.01919 1.363± 0.01067 10.0 8.253± 0.05823 2.792± 0.04602 20.0 17.89± 0.1114 5.27± 0.08448 50.0 49.31± 0.2473 13.3± 0.2008 75.0 77.2± 0.3849 20.37± 0.3553 100.0 103± 0.4574 27.55± 0.4024

TABLE G.5b MOKKA GEM - RESOLUTION DATA Eπ (GeV) Mean Energy (MeV) Sigma (MeV)

5.0 4.018± 0.0193 1.359± 0.0108 10.0 8.212± 0.0549 2.754± 0.04226 20.0 17.75± 0.1021 5.14± 0.07486 50.0 49.17± 0.2377 12.79± 0.1806 75.0 76.85± 0.369 19.86± 0.3217 100.0 102.7± 0.4492 27.04± 0.3787

TABLE G.6 MOKKA GEM – FEASIBILITY OF DIGITAL STUDY

Incident Pion Energy (GeV)

Mean number of cells Mean number of cells

3.0 27.24± 0.2477 28.75± 0.1508 5.0 50.51± 0.1426 50.03± 0.2083 10.0 97.51± 0.2158 97.77± 0.2147 18.0 166.7± 0.3498 166.6± 0.3499 25.0 222.2± 0.4568 221.5± 0.4453 38.0 318.8± 0.821 313.9± 0.7254 50.0 398.1± 1.077 389.3± 1.0199 65.0 487.9± 1.803 472.9± 1.411 80.0 570.6± 2.366 549± 1.839

129

TABLE G.7 MOKKA GEM – WEIGHTING FACTOR – DIGITAL STUDY Incident Pion Energy

(GeV) Mean Energy in EM

(MeV) Mean Energy in HC

(MeV) 1.0 23.93± 0.1341 93.02± 27.24 1.75 38.96± 0.303 162.4± 1.917 2.5 55.46± 0.54 260.7± 2.241 3.0 75.88± 0.5067 313.4± 2.911 4.0 101.2± 0.5346 402.5± 2.069 5.0 121.8± 0.707 539.9± 2.817 10.0 238.9± 3.275 1104± 6.226 20.0 526.6± 9.422 2129± 9.667 50.0 1467± 77.92 4935± 18.04 75.0 2037± 148.2 7013± 21.76 100.0 2800± 155.1 8924± 27.77

TABLE G.8 MOKKA GEM - RESPONSE DATA – DIGITAL STUDY

Incident Pion Energy (GeV)

Mean Energy (MeV) Mean Energy (MeV)

5.0 113.7± 0.3624 109.8± 0.959 10.0 236.8± 0.8845 223.4± 3.905 20.0 476.7± 0.9493 476.3± 3.26 50.0 1152± 2.453 1185± 5.852 75.0 1663± 3.136 1683± 4.526 100.0 2130± 3.996 2160± 5.913

TABLE G.9a MOKKA GEM - RESOLUTION DATA – DIGITAL STUDY

Incident Pion Energy (GeV)

Mean Energy (MeV) Sigma (MeV)

5.0 4.995± 0.01608 1.506± 0.01236 10.0 10.38± 0.03874 2.528± 0.02528 20.0 20.97± 0.04135 3.775± 0.02741 50.0 50.74± 0.1077 6.023± 0.06767 75.0 73.25± 0.1376 8.785± 0.1146 100.0 93.81± 0.176 11.17± 0.1474

130

TABLE G.9b MOKKA GEM - RESOLUTION DATA – DIGITAL STUDY Incident Pion Energy

(GeV) Mean Energy (MeV) Sigma (MeV)

5.0 4.825± 0.0324 1.569± 0.5362 10.0 10.18± 0.04785 2.784± 0.04911 20.0 20.98± 0.04826 3.974± 0.0448 50.0 51.69± 0.134 6.559± 0.1608 75.0 73.82± 0.1519 8.411± 0.1586 100.0 94.93± 0.2533 9.946± 0.3568

TABLE G.10 MOKKA GEM – DATA FOR THE CALCULATION OF

WEIGHTING FACTOR – DIGITAL STUDY WITH THRESHOLD APPLIED Incident Pion Energy

(GeV) Mean Energy in EM

(MeV) Mean Energy in HC

(MeV) 4.0 98.75± 0.4876 346.7± 1.88 5.0 120.1± 0.6607 459± 2.417 10.0 238.8± 2.312 961± 5.044 20.0 511.7± 5.061 1823± 6.089 50.0 1381± 85.67 4235± 15.55

TABLE G.11 MOKKA GEM - RESPONSE DATA – DIGITAL STUDY WITH

THRESHOLD APPLIED Incident Pion Energy

(GeV) Mean Energy (MeV) Mean Energy (MeV)

4.0 95.02± 0.2849 90.8± 0.3725 5.0 116.1± 0.3863 111.3± 0.6254 10.0 243.5± 0.9451 230.9± 2.176 20.0 490.6± 0.9852 487.8± 2.671 50.0 1197± 2.554 1222± 3.899 75.0 1726± 3.275 1747± 3.936 100.0 2215± 4.064 2239± 5.678

131

TABLE G.12a MOKKA GEM - RESOLUTION DATA – DIGITAL STUDY WITH THRESHOLD APPLIED

Incident Pion Energy (GeV)

Mean Energy (MeV) Sigma (MeV)

4.0 4.115± 0.01239 1.179± 0.008256 5.0 5.027± 0.01669 1.526± 0.01276 10.0 10.54± 0.04146 2.568± 0.0256 20.0 21.28± 0.0429 3.905± 0.02656 50.0 51.73± 0.1108 6.705± 0.08436 75.0 74.7± 0.1416 8.777± 0.1152 100.0 95.88± 0.1768 11.27± 0.1557

TABLE G.12b MOKKA GEM - RESOLUTION DATA – DIGITAL STUDY WITH

THRESHOLD APPLIED Incident Pion Energy

(GeV) Mean Energy (MeV) Sigma (MeV)

4.0 3.93± 0.01642 1.316± 0.01928 5.0 4.793± 0.03449 1.611± 0.05452 10.0 9.999± 0.09234 3.079± 0.1425 20.0 21.28± 0.06664 4.386± 0.08244 50.0 53.25± 0.259 7.155± 0.3717 75.0 75.61± 0.1768 8.423± 0.2148 100.0 96.61± 0.1988 10.22± 0.2219

TABLE G.13 MOKKA GEM - RESPONSE DATA – DIGITAL STUDY WITH

THRESHOLD APPLIED – A NONLINEAR APPROACH Incident Pion Energy

(GeV) Mean Energy (MeV) Mean Energy (MeV)

4.0 82.65± 0.2574 77.47± 0.5007 5.0 100.9± 0.3233 90.98± 2.743 10.0 205.4± 0.7609 199.2± 2.162 20.0 448.5± 1.039 434.3± 2.5 50.0 1235± 3.337 1283± 11.65 75.0 1857± 4.205 1907± 7.477 100.0 2364± 3.776 2470± 18.28

132

TABLE G.14a MOKKA GEM - RESOLUTION DATA – DIGITAL STUDY WITH THRESHOLD APPLIED – A NONLINEAR APPROACH

Incident Pion Energy (GeV)

Mean Energy (MeV) Sigma (MeV)

4.0 3.43± 0.01068 0.9896± 0.007222 5.0 4.174± 0.01348 1.244± 0.009733 10.0 8.527± 0.03186 2.119± 0.02169 20.0 18.6± 0.0433 3.751± 0.02692 50.0 51.09± 0.1416 8.371± 0.09876 75.0 77.06± 0.1766 9.511± 0.1258 100.0 98.09± 0.1572 9.167± 0.1434

TABLE G.14b MOKKA GEM - RESOLUTION DATA – DIGITAL STUDY WITH

THRESHOLD APPLIED –A NONLINEAR APPROACH Incident Pion Energy

(GeV) Mean Energy (MeV) Sigma (MeV)

4.0 3.222± 0.02391 1.126± 0.03837 5.0 3.79± 0.1081 1.856± 0.2037 10.0 8.237± 0.09262 2.359± 0.185 20.0 18.1± 0.08703 4.462± 0.1386 50.0 53.57± 0.6234 10.44± 1.003 75.0 79.1± 0.2628 9.48± 0.3752 100.0 102.1± 0.6459 10.02± 0.7147

TABLE G.15 OUTER LAYER ENERGY DEPOSIT IN MOKKA GEM

Eπ OLED (MeV) Number of Events

Total Energy Deposited

1.0 4.961e+01 10000 49754 1.75 8.612e+01 10000 478323 2.5 9.009e+02 10000 808159 3 5.634e+02 9977 867546 4 1.098e+02 10000 137443 5 1.733e+02 10000 1933291 10 6.830e+03 5000 2704643 20 3.283e+04 5000 6267889 50 1.445e+05 5000 18801649 75 2.656e+05 5000 29272121 100 4.120e+05 5000 39476918

133

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135

BIOGRAPHICAL INFORMATION

Shahnoor Habib was born in India and raised in Pakistan. She finished her

bachelors in mechanical engineering in 1988 and masters in nuclear

engineering in 1990. She has worked as a computer programmer for 8 years

and now is finishing her master of science in physics at UTA.

Her interests are reading books, watching movies and listening music.