PENELOPE 2003 - OECD Nuclear Energy Agency

TABLE OF CONTENTS
Foreword ........................................................................................................................................... iii
Preface ............................................................................................................................................... ix
1. Monte Carlo simulation. Basic concepts................................................................................. 1
1.1 Elements of probability theory............................................................................................ 2
1.1.1 Two-dimensional random variables.......................................................................... 5
1.2 Random sampling methods................................................................................................. 6
1.2.1 Random number generator ....................................................................................... 6
1.2.2 Inverse transform method ......................................................................................... 7
1.2.3 Discrete distributions................................................................................................ 10
1.2.4 Rejection methods .................................................................................................... 13
1.2.5 Two-dimensional variables. Composition methods.................................................. 15
1.3 Monte Carlo integration...................................................................................................... 18
1.4 Simulation of radiation transport ........................................................................................ 21
1.4.1 Scattering model and probability distributions......................................................... 21
1.4.2 Generation of random tracks..................................................................................... 24
1.4.3 Particle transport as a Markov process ..................................................................... 26
1.5 Statistical averages and uncertainties.................................................................................. 28
1.6 Variance reduction .............................................................................................................. 30
1.6.1 Interaction forcing .................................................................................................... 31
1.6.2 Splitting and Russian roulette................................................................................... 32
1.6.3 Other methods........................................................................................................... 33
2. Photon interactions................................................................................................................... 35
2.1 Coherent (Rayleigh) scattering ........................................................................................... 36
2.1.1 Simulation of coherent scattering events.................................................................. 39
2.2 Photoelectric effect ............................................................................................................. 40
2.2.1 Simulation of photoelectron emission ...................................................................... 42
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