PENELOPE 2003 - OECD Nuclear Energy Agency

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-