The mathematical technique of Monte Carlo, as applied to the transport of sub-atomic particles, has been described in numerous reports and books since its formal development in the 1940s. Most of these instructional efforts have been directed either at the mathematical basis of the technique or at its practical application as embodied in the several large, formal computer codes available for performing Monte Carlo transport calculations. This book attempts to fill what appears to be a gap in this Monte Carlo literature between the mathematics and the software. Thus, while the mathematical basis for Monte Carlo transport is covered in some detail, emphasis is placed on the application of the technique to the solution of practical radiation transport problems. This is done by using the PC as the basic teaching tool. This book assumes the reader has a knowledge of integral calculus, neutron transport theory, and Fortran programming. It also assumes the reader has available a PC with a Fortran compiler. Any PC of reasonable size should be adequate to reproduce the examples or solve the exercises contained herein. The authors believe it is important for the reader to execute these examples and exercises, and by doing so to become accomplished at preparing appropriate software for solving radiation transport problems using Monte Carlo. The step from the software described in this book to the use of production Monte Carlo codes should be straightforward.
This book introduces the reader to the use of Monte Carlo methods for solving practical problems in radiation transport, and will also serve as a reference work for practitioners in the field. It assumes the reader has a general knowledge of calculus and radiation physics, and a knowledge of Fortran programming, but assumes no prior knowledge of stochastic methods or statistical physics. The subject is presented by a combination of theoretical development and practical calculations. Because Monte Carlo methods are closely linked to the use of computers, from the beginning the reader is taught to convert the theoretical constructs developed in the text into functional software for use on a personal computer. Example problems provide the reader with an in-depth understanding of the concepts presented and lead to the production of a unique learning tool, a probabilistic framework code that models in a simple manner the features of production of Monte Carlo transport codes.This framework code is developed in stages such that every function is understood, tested, and demonstrated - random sampling, generating random numbers, implementing geometric models, using variance reduction, tracking particles in a random walk, testing the thoroughness with which the problem phase space is sampled, scoring detectors, and obtaining estimates of uncertainty in results.
Advanced topics covered include criticality, correlated sampling, adjoint transport, and neutron thermalization. Monte Carlo codes can produce highly precise wrong answers. The probability of this occurring is increased if production codes are run as opaque, 'black boxes' of software. This text attempts to make Monte Carlo into a comprehensible, usable tool for solving practical transport problems. It is suitable for advanced undergraduate and graduate students and researchers who wish to expand their knowledge of the Monte Carlo technique.
