A Monte Carlo Primer

1. Introduction.- 1.1 The Monte Carlo Method.- 1.2 The Evaluation of Random Processes>.- 1.3 Monte Carlo Evaluation of Definite Integrals.- Exercises.- 2. Monte Carlo Sampling Techniques.- 2.1 Probability Theory and Statistics.- 2.2 Sampling.- 2.3 Means and Variances.- 2.4 Estimations of Means and Variances.- 2.5 Introduction to Variance Reduction Techniques.- Exercises.- 3. Monte Carlo Modeling of Neutron Transport.- 3.1 Introduction.- 3.2 Neutron Interactions and Mean Free Path.- 3.3 Neutron Transport.- 3.4 A Mathematical Basis for Monte Carlo Neutron Transport.- 3.5 Monte Carlo Modeling of Neutron Motion.- 3.6 Particle Flight Path in Complex Geometries.- 3.7 Multi-Region Problems.- Exercises.- 4. Energy-Dependent Neutron Transport.- 4.1 Elastic Scattering of Neutrons.- 4.2 Transformation of Post-Collision Direction to Laboratory System.- 4.3 Energy-Dependent Cross Sections.- Exercises.- 5. A Probabilistic Framework Code.- 5.1 Introduction to PFC.- 5.2 Problem Definition in PFC.- 5.3 The Random Walk in PFC.- 5.4 Computing the Response.- Exercises.- 6. Variance Reduction Techniques.- 6.1 Introduction.- 6.2 Source Biasing.- 6.3 Survival Biasing.- 5.4 Russian Roulette.- 6.5 Splitting.- 6.6 Exponential Transform.- Exercises.- 7. Monte Carlo Detectors.- 7.1 Introduction.- 7.2 The Next-Event Estimator.- 7.3 Volumetric Flux Detectors.- 7.3 Surface-Crossing Flux Estimator.- 7.5 Expectation Surface-Crossing Flux Estimator.- Time-Dependent Detectors.- Exercises.- 8. Nuclear Criticality Calculations with Monte Carlo.- 8.1 Multiplying Assemblies.- 8.2 The Generation Method.- 8.3 The Matrix Method.- 8.4 Combination of Generation and Matrix Methods.- 8.5 Criticality Calculations Using Multigroup Cross Sections.- Exercises.- 9. Advanced Applications of Monte Carlo.- 9.1 Correlated Sampling.- 9.2 Adjoint Monte Carlo.- 9.3 Neutron Thermalization.- Exercises.- Appendix Random Number Generators.