PENELOPE 2003 - OECD Nuclear Energy Agency

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152 Chapter 4. Electron/positron transport mechanics only by statistical uncertainties. In general, our mixed simulation algorithm yields very accurate results (i.e. agreeing with those from detailed simulation) for electron and positron transport in infinite media, but not necessarily for limited geometries. The existence of interfaces poses considerable problems to condensed (class I) simulation, for which a satisfactory solution/approximation is not yet known. The present mixed (class II) algorithm handles interface crossing in a more accurate, but still approximate way. The rule to ensure accuracy for transport in the vicinity of interfaces is to use a small enough value of s max .
Chapter 5 Constructive quadric geometry Practical simulations of radiation transport in material systems involve two different kinds of operations, namely, physical (determination of the path length to the next interaction, random sampling of the different interactions) and geometrical (space displacements, interface crossings, . . . ). In the case of material systems with complex geometries, geometrical operations can take a large fraction of the simulation time. These operations are normally performed by dedicated subroutine packages, whose characteristics depend on the kind of algorithm used to simulate the interactions. The material system is assumed to consist of a number of homogeneous bodies limited by well-defined surfaces. The evolution of particles within each homogeneous body is dictated by the physical simulation routines, which operate as if particles were moving in an infinite medium with a given composition. Normally, the physical routines can handle a number of different media, whose interaction properties have been previously stored in memory. The job of the geometry routines is to steer the simulation of particle histories in the actual material system. They must determine the active medium, change it when the particle crosses an interface (i.e. a surface that separates two different media) and, for certain simulation algorithms, they must also keep control of the proximity of interfaces. In this chapter we describe the fortran subroutine package pengeom, which is adequate for detailed simulation algorithms (i.e. algorithms where all single interactions in the history of a particle are simulated in chronological succession). With these algorithms, the description of interface crossings is very simple: when the particle reaches an interface, its track is stopped just after entering a new material body and restarted again with the new active medium. This method (stopping and restarting a track when it crosses an interface) is applicable even when we have the same medium on both sides of the surface. That is, detailed simulations with a single homogeneous body and with the same body split into two parts by an arbitrary surface yield the same results (apart from statistical uncertainties). As we have seen, detailed simulation is feasible only for photon transport and lowenergy electron transport. For high-energy electrons and positrons, most Monte Carlo codes [e.g. etran (Berger and Seltzer, 1988), its3 (Halbleib et al., 1992), egs4 (Nel-
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Data Bank ISBN 92-64-02145-0 PENELO
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FOREWORD The OECD/NEA Data Bank was
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TABLE OF CONTENTS Foreword ........
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4.3 Combined scattering and energy
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PREFACE Radiation transport in matt
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The present version of PENELOPE is
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Chapter 1 Monte Carlo simulation. B
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1.1. Elements of probability theory
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1.1. Elements of probability theory
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1.2. Random sampling methods 7 Tabl
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1.2. Random sampling methods 9 Nume
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1.2. Random sampling methods 11 whe
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1.2. Random sampling methods 13 can
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1.2. Random sampling methods 15 mus
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1.2. Random sampling methods 17 the
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1.3. Monte Carlo integration 19 Con
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1.4. Simulation of radiation transp
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¡ ¢ 1.4. Simulation of radiation
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1.5. Statistical averages and uncer
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1.6. Variance reduction 31 also imp
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1.6. Variance reduction 33 weight a
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Chapter 2 Photon interactions In th
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2.1. Coherent (Rayleigh) scattering
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2.1. Coherent (Rayleigh) scattering
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2.2. Photoelectric effect 41 ➤E E
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F 2.2. Photoelectric effect 43 1E+7
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2.3. Incoherent (Compton) scatterin
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C u 2.3. Incoherent (Compton) scatt
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2.4. Electron-positron pair product
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2.5. Attenuation coefficients 63 di
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2.6. Atomic relaxation 65 2.6 Atomi
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2.6. Atomic relaxation 67 two vacan
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Chapter 3 Electron and positron int
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3.1. Elastic collisions 71 nucleus
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3.1. Elastic collisions 73 1 E - 1
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ρ ρ ρ λ λ λ ρ ρ ρ λ λ λ
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3.1. Elastic collisions 77 becomes
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B ' B ' 3.1. Elastic collisions 79
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3.2. Inelastic collisions 81 where
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3.2. Inelastic collisions 83 global
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3.2. Inelastic collisions 85 plays
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3.2. Inelastic collisions 87 optica
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3.2. Inelastic collisions 89 The DC
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3.2. Inelastic collisions 91 In the
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3.2. Inelastic collisions 93 where
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c b c b 3.2. Inelastic collisions 9
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A l A u 3.2. Inelastic collisions 9
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3.2. Inelastic collisions 99 After
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Page 119 and 120: 3.3. Bremsstrahlung emission 107 an
Page 121 and 122: 3.3. Bremsstrahlung emission 109 1
Page 123 and 124: 3.3. Bremsstrahlung emission 111 1
Page 125 and 126: 3.3. Bremsstrahlung emission 113 wh
Page 127 and 128: 3.3. Bremsstrahlung emission 115 Al
Page 129 and 130: 3.3. Bremsstrahlung emission 117 Th
Page 131 and 132: 3.4. Positron annihilation 119 (198
Page 133 and 134: 3.4. Positron annihilation 121 It i
Page 135 and 136: Chapter 4 Electron/positron transpo
Page 137 and 138: 4.1. Elastic scattering 125 Lewis (
Page 139 and 140: 4.1. Elastic scattering 127 ⎡ ⎛
Page 141 and 142: 4.1. Elastic scattering 129 simulat
Page 143 and 144: 4.1. Elastic scattering 131 The sim
Page 145 and 146: 4.2. Soft energy losses 133 soft in
Page 147 and 148: 4.2. Soft energy losses 135 deviati
Page 149 and 150: 4.2. Soft energy losses 137 scatter
Page 151 and 152: 4.3. Combined scattering and energy
Page 159 and 160: 4.4. Generation of random tracks 14
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Page 167 and 168: 5.1. Rotations and translations 155
Page 169 and 170: 5.2. Quadric surfaces 157 Given a f
Page 171 and 172: 5.2. Quadric surfaces 159 Table 5.1
Page 173 and 174: 5.3. Constructive quadric geometry
Page 175 and 176: 5.4. Geometry definition file 163 1
Page 177 and 178: 5.4. Geometry definition file 165
Page 179 and 180: 5.5. The subroutine package pengeom
Page 181 and 182: 5.5. The subroutine package pengeom
Page 183 and 184: 5.6. Debugging and viewing the geom
Page 185 and 186: 5.7. A short tutorial 173 MODULE (
Page 187 and 188: 5.7. A short tutorial 175 Writing a
Page 189 and 190: Chapter 6 Structure and operation o
Page 191 and 192: 6.1. penelope 179 and/or numbers in
Page 193 and 194: 6.1. penelope 181 1986). The format
Page 195 and 196: 6.1. penelope 183 The connection of
Page 197 and 198: 6.1. penelope 185 that has to be lo
Page 199 and 200: G y y y y y 6.1. penelope 187 CALL
Page 201 and 202: 6.1. penelope 189 It is the respons
Page 203 and 204: 6.2. Examples of MAIN programs 191
Page 213 and 214: 6.3. Selecting the simulation param
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! 6.3. Selecting the simulation par
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6.5. Installation 205 radiation is
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6.5. Installation 207 To get the ex
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Appendix A Collision kinematics To
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A.1. Two-body reactions 211 Clearly
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A.2. Inelastic collisions of charge
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m A.2. Inelastic collisions of char
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Appendix B Numerical tools B.1 Cubi
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B.1. Cubic spline interpolation 219
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B.2. Numerical quadrature 221 B.2 N
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Appendix C Electron/positron transp
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C.1. Tracking particles in vacuum.
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C.1. Tracking particles in vacuum.
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C.2. Exact tracking in homogeneous
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C.2. Exact tracking in homogeneous
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Bibliography Abramowitz M. and I.A.
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Bibliography 235 Briesmeister J.F.
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Bibliography 237 James F. (1990),
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Bibliography 239 Reimer L. and E.R.
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Bibliography 241 Yates A.C. (1968),
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