PENELOPE 2003 - OECD Nuclear Energy Agency

204 Chapter 6. Structure and operation of the code system
The maximum allowed step length s max (denoted by DSMAX in the fortran source
files) should be less than one tenth of the characteristic thickness of the body where the
particle moves. This ensures that, on average, there will be more than 20 soft events 4
(hinges) along a typical electron/positron track within that body, which is enough to
“wash out” the details of the artificial distributions used to sample these events. Notice
however that penelope internally forces the step length to be less than ∼ 3λ (h)
T (see
section 4.4). Therefore, for thick bodies (thicker than ∼ 20λ (h)
T ), we can set s max = 10 35 ,
or some other very large value, to switch off the external step-length control.
The MAIN program PENSLAB can be readily used to study the effect of the simulation
parameters for a material body of a given characteristic thickness. As an example, figs.
6.5 and 6.6 display partial results from a PENSLAB simulation for a parallel electron
beam of 500 keV impinging normally on the surface of a 200-µm-thick aluminium slab.
The absorption energies were set equal to 10 keV (for all kinds of particles) and W cr
was given a negative value, which compels penelope to set W cr = 10 eV and to
disregard emission of soft bremsstrahlung (with W < 10 eV). We ran PENSLAB using
W cc = 0 and C 1 = C 2 = 0; in this case, penelope performs purely detailed, collision by
collision, simulation and, therefore, it provides exact results (affected only by statistical
uncertainties and by inaccuracies of the physical interaction model). Differences between
these results and those from mixed simulation are then completely attributable to the
approximations in our mixed transport algorithm. To our knowledge, no other highenergy
transport code allows detailed simulation and this kind of direct validation of
the electron/positron transport mechanics.
In figs. 6.5 and 6.6 we compare results from the detailed simulation (7.5 million
showers) with those from a mixed simulation using W cc = 1 keV and C 1 = C 2 = 0.15
(20 million simulated showers); the error bars indicate statistical uncertainties (3σ).
With these relatively high values of C 1 and C 2 , mixed simulation is quite fast, the speed
(generated showers per second) being about 45 times higher than that of the detailed
simulation. As shown in the plots, mixed simulation results are practically equivalent
to those from detailed simulation. It should be noted that backscattering, fig. 6.6b, is
one of the most difficult cases to study, because it involves transport near and across
an interface that is far from electronic equilibrium. The only visible artifact is a kind
of singularity in the energy distribution of backscattered electrons at ∼250 keV (which
averages to the correct value and, therefore, would not be seen in a coarser energy grid).
This artifact is also present in the energy distribution of transmitted electrons, but
hardly visible in the scale of fig. 6.6a.
6.4 The code shower
Monte Carlo simulation has proven to be a very valuable tool for education. In the past,
radiation physics used to be considered as a tough subject, mostly because high-energy
4 penelope randomizes s max in such a way that the actual step lengths never exceeds the value s max
set by the user and, on average, is equal to s max /2.