PENELOPE 2003 - OECD Nuclear Energy Agency

Chapter 1
Monte Carlo simulation. Basic
concepts
The name “Monte Carlo” was coined in the 1940s by scientists working on the nuclear
weapon project in Los Alamos to designate a class of numerical methods based on the
use of random numbers. Nowadays, Monte Carlo methods are widely used to solve
complex physical and mathematical problems (James, 1980; Rubinstein, 1981; Kalos
and Whitlock, 1986), particularly those involving multiple independent variables where
more conventional numerical methods would demand formidable amounts of memory
and computer time. The book by Kalos and Whitlock (1986) gives a readable survey of
Monte Carlo techniques, including simple applications in radiation transport, statistical
physics, and many-body quantum theory.
In Monte Carlo simulation of radiation transport, the history (track) of a particle is
viewed as a random sequence of free flights that end with an interaction event where
the particle changes its direction of movement, loses energy and, occasionally, produces
secondary particles. The Monte Carlo simulation of a given experimental arrangement
(e.g. an electron beam, coming from an accelerator and impinging on a water phantom)
consists of the numerical generation of random histories. To simulate these histories we
need an “interaction model”, i.e. a set of differential cross sections (DCS) for the relevant
interaction mechanisms. The DCSs determine the probability distribution functions
(PDF) of the random variables that characterize a track; 1) free path between successive
interaction events, 2) kind of interaction taking place and 3) energy loss and angular
deflection in a particular event (and initial state of emitted secondary particles, if any).
Once these PDFs are known, random histories can be generated by using appropriate
sampling methods. If the number of generated histories is large enough, quantitative
information on the transport process may be obtained by simply averaging over the
simulated histories.
The Monte Carlo method yields the same information as the solution of the Boltzmann
transport equation, with the same interaction model, but is easier to implement
(Berger, 1963). In particular, the simulation of radiation transport in finite samples is