PENELOPE 2003 - OECD Nuclear Energy Agency

148 Chapter 4. Electron/positron transport mechanics
However, this is not the only reason for limiting the step length. Since energy losses
and deflections at the hinges are sampled from artificial distributions, the number of
hinges per primary track must be “statistically sufficient”, i.e. larger than ∼ 10, to
smear off the unphysical details of the adopted artificial distributions. Therefore, when
the particle is in a thin region, it is advisable to use a small value of s max to make
sure that the number of hinges within the material is sufficient. In penelope, the
parameter s max can be varied freely during the course of the simulation of a single
track. To ensure internal consistency, s max is required to be less than 3λ (h)
T . When
the user-selected value is larger, the code sets s max = 3λ (h)
T ; in this case, about 5 per
cent of the sampled steps have lengths that exceed s max and are terminated by a delta
interaction. This slows down the simulation a little (∼5%), but ensures that the energy
dependence of λ (h)
T is correctly accounted for. Instead of the s max value set by the user,
penelope uses a random maximum step length [from a triangle distribution in the
interval (0,s max )] that averages to half the user’s value; this is used to eliminate an
artifact in the depth-dose distribution from parallel electron/positron beams near the
entrance interface. Incidentally, limiting the step length is also necessary to perform
simulation of electron/positron transport in external static electromagnetic fields (see
appendix C).
The state of the particle immediately after an event is defined by its position coordinates
r, energy E and direction cosines of its direction of movement ˆd, as seen from
the laboratory reference frame. It is assumed that particles are locally absorbed when
their energy becomes smaller than a preselected value E abs ; positrons are considered to
annihilate after absorption. The practical generation of random electron and positron
tracks in arbitrary material structures, which may consist of several homogeneous regions
of different compositions separated by well-defined surfaces (interfaces), proceeds
as follows:
(i) Set the initial position r, kinetic energy E and direction of movement ˆd of the
primary particle.
(ii) Determine the maximum allowed soft energy loss ω max along a step and set the
value of inverse mean free path for hard events (see section 4.3). The results
depend on the adopted s max , which can vary along the simulated track.
(iii) Sample the distance s to be travelled to the following hard event (or delta interaction)
as
s = − ln ξ/Σ h,max . (4.119)
If s > s max , truncate the step by setting s = s max .
(iv) Generate the length τ = sξ of the step to the next hinge. Let the particle advance
this distance in the direction ˆd: r ← r + τ ˆd.
(v) If the track has crossed an interface:
Stop it at the crossing point (i.e. redefine r as equal to the position of this point
and set τ equal to the travelled distance).
Go to (ii) to continue the simulation in the new material, or go to (xi) if the new
material is the outer vacuum.
(vi) Simulate the energy loss and deflection at the hinge. This step consists of two
actions: