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34 CHAPTER 2. DETECTOR PHYSICS OF RPCS y cathode φ r x z=g z anode Figure 2.1: In our studies we will mainly use cylindrical coordinates z, r and φ, where the z-axis is perpendicular to the cathode and anode, that are situated at z = 0 and z = g. MAGBOLTZ [76], IMONTE [77] and HEED [25]. We start with a discussion of primary ionization processes (section 2.1), followed by diffusion, drift and the multiplication of electrons under the influence of an electric field (section 2.2). In section 2.3 we investigate the electrostatics of a three layer geometry like an RPC. There we present the analytic formulas that can be used to calculate the electric field contributions of the space charge. The signal generation process and the weighting field formalism are the topic of section 2.4 and finally we shortly discuss the phenomenon of streamers in section 2.5. Based on the knowledge summarized in this chapter we shall present Monte-Carlo simulation models for avalanches in RPCs in chapter 3. 2.1 Gas Ionization by Fast Charged Particles In the following sections we discuss the average distances between primary clusters, the effect on the detection efficiency of RPCs and the distribution of the number of released electrons per cluster.
2.1. GAS IONIZATION BY FAST CHARGED PARTICLES 35 2.1.1 Distance between Primary Clusters We assume that the probability of an ionizing collision does not depend on the previous collision, which is correct if the energy loss is negligible compared to the particle energy. In that case the distance between the ionizing collisions (the distance between primary clusters) is exponentially distributed like P (z) = 1 λ exp − z λ . (2.1) If σp(β) [cm 2 ] is the ionization cross section in a gas with density ρ, then the mean free path λ is given by λ = A ρNA 1 , (2.2) σp(β) where A is the atomic mass number of the gas [g/mol] and NA is Avogadro’s number [1/mol]. The ionization cross section of a particle with charge z in unit charges and velocity v = βc, where c is the speed of light, for different gases can be written as [75, 15] σp(β) = 4 π 2 z mc 2 (M 2 x1 + C x2) , (2.3) where 4 π (/mc) 2 =1.874×10 −20 cm 2 , M 2 and C are constants characteristic to the gas and x1 = 1 β 2 ln(β2 γ 2 ) − 1 , x2 = 1 β 2 , γ = 1 1 − β 2 . (2.4) As mentioned previously, the average distance between the clusters λ can be obtained using the simulation program HEED [25]. HEED is a Monte-Carlo model based on the photo-absorption ionization model by W.W.M. Allison and J.H. Cobb [78]. HEED data for two typical RPC gas mixtures and for pure isobutane and pure methane are shown in Fig. 2.2. The comparison of measurements for isobutane and methane shows good agreement of simulated and measured data. The measurements are from [75], where we find M 2 = 14.19 and C = 141.9 for isobutane and M 2 = 4.23 (3.69) and C = 41.85 (43.88) for methane, obtained with two different experimental methods.
Page 1 and 2: Detector Physics of Resistive Plate
Page 3 and 4: Zusammenfassung Widerstandsplattenk
Page 5 and 6: Abstract Resistive Plate Chambers (
Page 7 and 8: Contents 1 Introduction 1 1.1 Parti
Page 9 and 10: CONTENTS vii 7.2.3 Total Charge Den
Page 11 and 12: List of Figures 1.1 Schematic image
Page 13 and 14: LIST OF FIGURES xi 6.11 Simulated i
Page 15 and 16: Chapter 1 Introduction Resistive Pl
Page 17 and 18: 1.1. PARTICLE PHYSICS AND EXPERIMEN
Page 23 and 24: 1.2. INTERACTIONS OF PARTICLES WITH
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Page 39 and 40: 1.4. TRIGGER RPCS AND THEIR APPLICA
Page 41 and 42: 1.5. TIMING RPCS AND THEIR APPLICAT
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Page 45 and 46: 1.6. SUMMARY 31 on the Time-Of-Flig
Page 47: Chapter 2 Detector Physics of RPCs
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Page 71 and 72: 2.4. SIGNAL INDUCTION PROCESS 57 E
Page 73 and 74: 2.5. STREAMERS 59 Figure 2.20: A me
Page 75 and 76: 2.6. SUMMARY 61 per cluster follows
Page 77 and 78: Chapter 3 Monte Carlo Avalanche Sim
Page 79 and 80: 3.1. THE 1-D MODEL 65 Avalanche Siz
Page 81 and 82: 3.2. THE 1.5-D MODEL 67 3. The prim
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Page 85 and 86: 3.2. THE 1.5-D MODEL 71 charge [pC]
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Page 89 and 90: 3.2. THE 1.5-D MODEL 75 number of c
Page 91 and 92: 3.3. THE 2-D MODEL 77 where δt is
Page 93 and 94: 3.3. THE 2-D MODEL 79 Er(r, z, r
Page 95 and 96: 3.3. THE 2-D MODEL 81 y r E Er θ x
Page 97 and 98: 3.4. THE 3-D MODEL 83 The charge in
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3.4. THE 3-D MODEL 85 Electrons a)
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Chapter 4 Geometries and Typical Op
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RPC gas q [mm] g [mm] εr EW [/mm]
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The values shown in Table 4.3 are r
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Chapter 5 Results Obtained with the
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5.1. EFFICIENCY AND TIME RESOLUTION
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5.2. CHARGE-TO-TIME CORRELATION 97
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6.1. SIGNAL RISE TIME 101 induced c
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6.2. CHARGE SPECTRA 103 counts 10 3
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6.2. CHARGE SPECTRA 105 charges/ste
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6.2. CHARGE SPECTRA 107 The differe
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6.2. CHARGE SPECTRA 109 counts/35fC
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6.2. CHARGE SPECTRA 111 charges/ste
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6.3. OPERATIONAL MODE OF RPCS 113 t
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6.4. CHARGE-TO-TIME CORRELATION 115
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6.5. AVALANCHES IN PURE ISOBUTANE 1
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6.6. STREAMERS 121 a) b) electrons
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7.1. COMPARISON OF THE DIFFERENT MO
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7.2. AVALANCHES IN C2F4H2/ I-C4H10/
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7.4. SUMMARY 151 (e) The total elec
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7.4. SUMMARY 153 contracted at thei
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Chapter 8 Conclusions and Outlook C
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Appendix A Differential Collision C
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A.4. SCATTERING OF MASSIVE SPIN 1 P
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Appendix B Überblick Widerstandspl
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B.1. MOTIVATION FÜR DIE ARBEIT 163
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B.2. DETEKTORPHYSIK VON RPCS 165 i(
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B.4. SCHLUSSFOLGERUNG UND AUSBLICK
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Bibliography [1] W. Riegler, R. Vee
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BIBLIOGRAPHY 171 [29] V. Parchomchu
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BIBLIOGRAPHY 173 [59] E. Keil. The
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BIBLIOGRAPHY 175 [88] P. Fonte. App
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Danksagung Während der Dissertatio
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Curriculum Vitae Persönliche Infor
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